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All Textbook Solutions for Precalculus

For Exercises 63-84, solve the inequalities. (See Examples 4-5) 2z14zFor Exercises 63-84, solve the inequalities. (See Examples 4-5) 34x61xFor Exercises 63-84, solve the inequalities. (See Examples 4-5) 52x33xFor Exercises 63-84, solve the inequalities. (See Examples 4-5) 2x2x+12x440For Exercises 63-84, solve the inequalities. (See Examples 4-5) 3x4x14x+220A professional fireworks team shoots an 8-in. mortar straight upwards from ground level with an initial speed of 216 ft/sec. (See Example 7) a. Write a function modeling the vertical position s(t) (in ft) of the shell at a time t seconds after launch. b. The mortar is designed to explode when the Shell is at its maximum height. How long after launch will the Shell explode? c. The spectators can see the shell rising once it clears a 200-ft tree line. For what period of time after launch is the shell visible before it explodes?Suppose that a basketball player jumps straight up for a rebound. a If his initial speed leaving the ground is 16 ft/sec, write a function modeling his vertical position s(t) (in ft) at a tame t seconds after leasing the ground. b. Find the times after leaving the ground when the player will be at a height of more than 3 ft in the air.For a certain stretch of road, the distance d (in ft) required to stop a car that is traveling at speed v (in mph) before the brakes are applied can be approximated by dv=0.06v2+2v. Find the speeds for which the car can be stopped within 250 ft.The population Pt of a bacteria culture is given by Pt=1500t2+60,000t+10,000, here t is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 460,000 organisms.89PEThe average round trip speed 5inmph of a vehicle traveling a distance of d miles in each direction is given by S=2ddr1+dr2wherer1andr2aretheratesofspeedfortheinitaltripandthereturntrip,respectively. a. Suppose that a motorist travels 200 mi from her home to an athletic event and averages 50 mph for the trip to the event. Determine the speeds necessary if the motorist wants the average speed for the round trip to be at least 60 mph. b. Would the motorist be traveling within the speed limit of 70 mph?A rectangular quit is to be made so that the length is 1.2 times the width. The quilt must be between 72ft2and96ft2 to cover the bed. Determine the restrictions on the width so that the dimensions of the quilt will meet the required area. Give exact values and the approximated values to the nearest tenth of a foot.A landscaping team plans to build a rectangular garden that is between 480yd2and720yd2 in area. For aesthetic reasons, they also want the length to be 1.5 times the width. Determine the restrictions on the width so that the dimensions of the garden will meet the required area. Give exact values and the approximated values to the nearest tenth of a yard.For Exercises 93-102, write the domain of the function in interval notation. fx=9x2For Exercises 93-102, write the domain of the function in interval notation. gt=1t2For Exercises 93-102, write the domain of the function in interval notation. ha=a25For Exercises 93-102, write the domain of the function in interval notation. fu=u27For Exercises 93-102, write the domain of the function in interval notation. px=2x2+9x18For Exercises 93-102, write the domain of the function in interval notation. qx=4x2+7x2For Exercises 93-102, write the domain of the function in interval notation. rx=12x2+9x18For Exercises 93-102, write the domain of the function in interval notation. sx=14x2+7x2For Exercises 93-102, write the domain of the function in interval notation. hx=3xx+2For Exercises 93-102, write the domain of the function in interval notation. kx=2xx+1Let a,b,andc represent positive real numbers, where abc , and let fx=xa2bxxc3. a. Complete the sign chart. b. Solve fx0. c. Solve fx0.Let a,b,andc represent positive real numbers, where abc , and let gx=axxb2cx5. a. Complete the sign chart. b. Solve gx0. c. Solve gx0.Explain how the solution set to the inequality fx0 is related to the graph of y=fx.106PEExplain why x2+2x2+10 has no solution.108PE109PE110PEThe procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. 4x60The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. 5x70The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. 1x240The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. 1x350115PEThe procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. 8x2+4x+315The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. x245118PEThe procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. x2182The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form fx0,fx0,fx0,andfx0. That is, find the real solutions to the related equation and determine restricted value of x. Then determine the sign of fx on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. x263121PEGiven the inequality, 0.24x4+1.8x3+3.3x2+2.84x1.84.5, a Write the inequality in the form fx0. b. Graph y=fx on a suitable viewing window. c. Use the Zero feature to approximate the real zeros of fx. Round to 1 decimal place. d. Use the graph to approximate the solution set for the inequality fx0.An engineer for a food manufacturer designs an aluminum container for a hot drink mix. The container is to be a right circular 5.5 in. in height. The surface area represents the amount of aluminium used and is given by Sr=2r2+11r, where r is the radius of the can. a. Graph the function y=Sr and the line y=90 on the viewing window 0,3,1by0,150,10. b. Use the Intersect feature to approximate the point of intersection of y=Sr and y=90 .Round to 1 decimal place if necessary. c. Determine the restrictions on r so that the amount of aluminum used is at most 90in.2 Round to 1 decimal place.The concentration Ct (in ng/mL) of a drug in the bloodstream t hours after ingestion is modeled by Ct=500tt3+100 a. Graph the function y=Ct and the line y=4 on the window 0,32,4by0,15,3 . b. Use the Intersect feature to approximate the point(s) of intersection of y=Ctandy=4. Round to 1 decimal place if necessary. c. To avoid toxicity, a physician may give a second dose of the medicine once the concentration falls below 4 ng/mL for increasing values of t . Determine the times at which it is safe to give a second dose. Round to 1 decimal place.For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 1214x52For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 2x26x=5For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 50x325x22x+1=04PREFor Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. m+445=2For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 5yand3y+47For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 5t4+2=7For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 34x5x+232x=24x1For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 10x2x14=29x2100For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 5y4=3yy+22y214yy22y8For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. xx1440For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 1x214x+400For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. x0.15=x+0.05For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. t151For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. n1/2+7=10For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 4x3xx+22x530For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 2x5x+3=4x+23xFor Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 7x+293=xFor Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. x2925x2914=0For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 2+7x115x2=0For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 8x3+107For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 2x13/4=1623PREFor Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 3xx+51For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 153x1=2xx18For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 25x2+70x49For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 23x9For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 4x38or7x3For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 13x+2556x1For Exercises 1-30, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation if possible. 22x+128Write a variation model using k as the constant of variation. a. The distance d that a spring stretches varies directly as the force F applied to the spring. b. The force F required to keep a car from skidding on a curved road varies inversely as the radius r of the curve. c. The variable a varies directly as b and inversely as the cube root of c.Write a variable model using k as the constant of variation. a. The kinetic energy E of an object varies jointly as the object’s mass m and the square of its velocity v. b. z varies jointly as x and y and inversely as the square root of w.The amount of the medicine ampicillin that a physician prescribes for a child varies directly as the weight of the child. A physician prescribes 420 mg for a 35-lb child. a. How much should be prescribed for a 30-lb child? b. How much should be prescribed for a 40-lb child?The yield on a bond varies inversely as the price. The yield on a particular bond is 4 when the price is $100. Find the yield when the price is $80.The amount of simple interest earned in an account varies jointly as the interest rate and time of the investment. An account earns $200 in 2 yr at 4 interest. How much interest would be earned in 3 yr at a rate of 5?If k is a nonzero constant real number, then the statement y=kx implies that y varies as x.If k is a nonzero constant real number, then the statement y=kx implies that y varies as x.The value of k in the variation models y=kxandy=kx is called the of .If y varies directly as two or more other variables such as x and w, then y=kxw, and we say that y varies as x and w.a. Given y=2x, evaluate y for the given values of x:x=1,x=2,x=3,x=4,andx=5. b. How does y change when x is doubled? c. How does y change when x is tripled? d. Complete the statement. Given y=2x, when x increases, y (increases/decreases) proportionally. e. Complete the statement. Given y=2x, when x decreases, y (increases/decreases) proportionally.6PEThe time required to drive from Atlanta, Georgia, to Nashville, Tennessee, varies as the average speed at which a vehicle travels.The amount of a person’s paycheck varies as the number of hours worked.The volume of a right circular cone varies as the square of the radius of the cylinder and as the height of the cylinder.A student’s grade on a test varies as the number of hours the student spends studying for the test.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The circumference C of a circle varies directly as its radius r.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) Simple interest I on a loan or investment varies directly as the amount A of the loan.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The average cost per minute C for a flat rate cell phone plan is inversely proportional to the number of minutes used n.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The time of travel t is inversely proportional to the rate of travel r.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The volume V of a right circular cylinder varies jointly as the height h of the cylinder and as the square of the radius r of the cylinder.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The volume V of a rectangular solid varies jointly as the length l and width w of the solid.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The variable E is directly proportional to s and inversely proportional to the square root of n.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The variable n is directly proportional to the square of and inversely proportional to the square of E.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The variable c varies jointly as m and n and inversely as the cube of t.For Exercises 11-20, write a variation model using k as the constant of variation. (See Example 1-2) The variable d varies jointly as u and v and inversely as the cube root of T.For Exercises 21-26, find the constant of variation k. y varies directly as x. When x is 8, y is 20.For Exercises 21-26, find the constant of variation k. m varies directly as x. When x is 10, m is 42.For Exercises 21-26, find the constant of variation k. p is inversely proportional to q. When q is 18, p is 54.For Exercises 21-26, find the constant of variation k. T is inversely proportional to x. When x is 50, T is 200.For Exercises 21-26, find the constant of variation k. y varies jointly as w and v. When w is 40 and v is 0.2, y is 40.For Exercises 21-26, find the constant of variation k. N varies jointly as t and p. When t is 2 and p is 2.5, N is 15.The value of y equal 4 when x=10. Find y when x=5 if a. y varies directly as x. b. y varies inversely as x.The value of y equal 24 when x is 12. Find y when x=3 if a. y varies directly as x. b. y varies inversely as x.For Exercises 29-48, use a variation model to solve for the unknown value. The amount of a pain reliever that a physician prescribes for a child varies directly as the weight of the child. A physician prescribes 180 mg of the medicine for a 40-lb child. (See Example 3) a. How much medicine would be prescribed for a 50-lb child? b. How much would be prescribed for a 60-lb child? c. How much would be prescribed for a 70-lb child? d. If 135 mg of medicine is prescribed what is the weight of the child?For Exercises 29-48, use a variation model to solve for the unknown value. The number of people that a ham can serve varies directly as the weight of the ham. An 8-lb ham feeds 20 people. a. How many people will a 10-lb ham serve? b. How many people will a 15-lb ham serve? c. How many people will an 18-lb ham serve? d. If a ham feeds 30 people, what is the weight of the ham?For Exercises 29-48, use a variation model to solve for the unknown value. A rental car company charges a fixed amount to rent a car per day. Therefore, the cost per mile to rent a car for a given day is inversely proportional to the number of miles driven. if 100 mi is driven, the average daily cost is $0.80 per mile. a. Find the cost per mile if 200 mi is driven. b. Find the cost per mile if 300 mi is driven. c. Find the cost per mile if 400 mi is driven. d. If the cost per mile is $0.16, how many miles were driven?For Exercises 29-48, use a variation model to solve for the unknown value. A chef self-publishes a cookbook and finds that the number of books she can sell per month varies inversely as the price of the book. The chef can sell 1500 books per month when the price is set at $8 per book. a. How many books would she expect to sell per month if the price were $12? b. How many books would she expect to sell pet month if the price were $15? c. How many books would she expect to sell per month if the price were $6? d. If the chef sells 1200 books, what price was set?For Exercises 29-48, use a variation model to solve for the unknown value. The distance that a bicycle travels in 1 min varies directly as the number of revolutions per minute (rpm) that the wheels are turning. A bicycle with a 14-in. radius travels approximately 440 ft in 1 min if the wheels turn at 60 rpm. How far will the bicycle travel in 1 min if the wheels turn at 87 rpm?For Exercises 29-48, use a variation model to solve for the unknown value. The amount of pollution entering the atmosphere varies directly as the number of people living in an area. If 100,000 people create 71,000 tons of pollutants, how many tons enter the atmosphere in a city with 750,000 people?For Exercises 29-48, use a variation model to solve for the unknown value. The stopping distance of a car is directly proportional to the square of the speed of the car a. If a car traveling 50 mph has a stopping distance of 170 ft, find the stopping distance of a car that is traveling 70 mph. b. If it takes 244.8 ft for a car to slop, how fast was it traveling before the brakes were applied?For Exercises 29-48, use a variation model to solve for the unknown value. The area of a picture projected on a wall varies directly as the square of the distance from the projector to the wall. a. If a 15-ft distance produces a 36ft2 picture, what is the area of the picture when the projection unit is moved to a distance of 25 ft from the wall? b. If the projected image is 144ft2 , how far is the projector from the wall?For Exercises 29-48, use a variation model to solve for the unknown value. The time required to complete a job varies inversely as the number of people working on the job. It takes 8 people 12 days to do a job. (See Example 4) a. How many days will it take if 15 people work on the job? b. If the contractor wants to complete the job in 8 days, how many people should work on the job?For Exercises 29-48, use a variation model to solve for the unknown value. The yield on a bond varies inversely as the price. The yield on a particular bond is 5 when the price is $120. a. Find the yield when the price is $100. b. What price is necessary for a yield of 7.5?For Exercises 29-48, use a variation model to solve for the unknown value. The current in a wire varies directly as the voltage and inversely as the resistance. If the current is 9 amperes (A) when the voltage is 90 volts (V) and the resistance is 10 ohms , find the current when the voltage is 160 V and the resistance is 5 .For Exercises 29-48, use a variation model to solve for the unknown value. The resistance of a wire varies directly as its length and inversely as the square of its diameter. A 50-ft wire with a 0.2-in. diameter has a resistance of 0.0125 . Find the resistance of a 40-ft wire with a diameter of 0.1 in.For Exercises 29-48, use a variation model to solve for the unknown value. The amount of simple interest owed on a loan varies jointly as the amount of principal borrowed and the amount of time the money is borrowed. If $4000 in principal results in $480 in interest in 2 yr, determine how much interest will be owed on $6000 in 4 yr.For Exercises 29-48, use a variation model to solve for the unknown value. The amount of simple interest earned in an account varies jointly as the amount of principal invested and the amount of time the money is invested. If $5000 in principal earns $750 in 6 yr, determine how much interest will be earned on $8000 in 4 yr.For Exercises 29-48, use a variation model to solve for the unknown value. The body mass index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the Individual. The body mass index for a 150-lb person who is 70 in. tall is 21.52. Determine the BMI for an individual who is 68 in. tall and 180 lb. Round to 2 decimal places. (See Example 5)For Exercises 29-48, use a variation model to solve for the unknown value. The strength of a wooden beam varies jointly as the width of the beam and the square of the thickness of the beam, and inversely as the length of the beam. A beam that is 48 in. long, 6 in. wide, and 2in. thick hoe can support a load of 417 lb. Find the maximum load that can be safely supported by a board that is 12 in. wide, 72 in. long, and 4 in thick.For Exercises 29-48, use a variation model to solve for the unknown value. The speed of a racing canoe in still water varies directly as the square root of the length of the canoe. A 16-ft canoe can travel 6.2 mph in still water. Find the speed of a 25-ft canoe.For Exercises 29-48, use a variation model to solve for the unknown value. The period of a pendulum is the length of time required to complete one swing back and forth. The period varies directly as the square root of the length of the pendulum. If it takes 1.8 sec for a 0.81-m pendulum to complete one period, what is the period, what is the period of a 1-m pendulum?For Exercises 29-48, use a variation model to solve for the unknown value. The cost to carpet a rectangular room varies jointly as the length of the room and the width of the room. A 10-yd by 15-yd room costs $3870 to carpet. What is the cost to carpet a room that is 18 yd by 24 yd?For Exercises 29-48, use a variation model to solve for the unknown value. The cost to tile a rectangular kitchen varies jointly as the length of the kitchen and the width of the kitchen. A 10-ft by 12-ft kitchen costs $1104 to tile. How much will it cost to tile a kitchen that is 20 ft by 14 ft?For Exercises 49-52, use the given data to find a variation model relating y to x.For Exercises 49-52, use the given data to find a variation model relating y to x.For Exercises 49-52, use the given data to find a variation model relating y to x.For Exercises 49-52, use the given data to find a variation model relating y to x.Which formula(s) can represent a variation model? a.y=kxyzb.y=kx+yzc.y=kxyzd.y=kxyzWhich formula(s) can represent a variation model? a.y=kxz2b.y=kxz2c.y=kxz2d.y=k+xz2For Exercises 55-56, write a statement in words that describes the variation model given. Use k as the constant of variation. P=kv2tFor Exercises 55-56, write a statement in words that describes the variation model given. Use k as the constant of variation. E=kc2bThe light from a lightbulb radiates outward in all directions. a. Consider the interior of an imaginary sphere on which the light shines. The surface area of the sphere is directly proportional to the square of the radius. If the surface area of a sphere with a 10-m radius is 400m2, determine the exact surface area of a sphere with a 20-m radius. b. Explain how the surf ace area changed when the radius of the sphere increased from 10 m to 20 m. c. Based on your answer from part (b) how would you expect the intensity of light to change from a point 10 m from the lightbulb to a point 20 m from the lightbulb? d. The intensity of light from a light source varies inversely as the square of the distance from the source. If the intensity of a lightbulb is 200 lumen/m2 (lux) at a distance of 10 m, determine the intensity at 20 m.Kepler's third law states that the square of the time T required for a planet to complete one orbit around the Sun is directly proportional to the cube of the average distance d of the planet to the Sun. For the Earth assume that d=9.3107miandT=365days. a. Find the period of Mars, given that the distance between Mars and the Sun is 1.5 times the distance from the Earth to the Sun. Round to the nearest day. b. Find the average distance of Venus to the Sun, given that Venus revolves around the Sun in 223 days. Round to the nearest million miles.The intensity of radiation varies inversely as the square of the distance from the source to the receiver. If the distance is increased to 10 times its original value, what is the effect on the intensity to the receiver?Suppose that y varies inversely as the cube of x. If the value of x is decreased to 14 of its original value, what is the effect on y?Suppose that y varies directly as x2 and inversely as w4 . If both x and w are doubled, what is the effect on y?Suppose that y varies directly as x5 and inversely as w2 . If both x and w are doubled, what is the effect on y?Suppose that y varies jointly as x and w3. . If x is replaced by 13x and w is replaced by 3w, what is the effect on y?Suppose that y varies jointly as x4 and w. If x is replaced by 14x and w is replaced by 4w, what is the effect on y?For Exercises 1-2, determine if the relation defines y as a one-to-one function of x.For Exercises 1-2, determine if the relation defines y as a one-to-one function of x.3RE4RE5RE6RE7RE8REa. Graph fx=x29,x0. b. Is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Find an equation for f1. f. Graph y=fxandy=f1x on the same coordinate system. g. Write the domain of f1 in interval notation. h. Write the range of f1 in interval notation.10RE11RE12RE13REFor Exercises 13-16, a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. d. Write an equation of the asymptote. gx=52x15RE16RE17RE18RE19REA patient is treated with 128 mCi (millicuries) of iodine-131131I. The radioactivity level Rt (in mCi) after t days is given by Rt=1282t/4.2. (In this model, the value 4.2 is related to the biological half-life of radioactive iodine in the body.) a. Determine the radioactivity level of 131I in the body after 6 days. Round to the nearest whole unit. b. Evaluate R4.2 and interpret its meaning in the context of this problem. c. After how many half-lives will the radioactivity level be 16 mCi?21RE22RE23RE24REFor Exercises 25-32, simplify the logarithmic expression without using a calculator. log381For Exercises 25-32, simplify the logarithmic expression without using a calculator. log100,000For Exercises 25-32, simplify the logarithmic expression without using a calculator. log216428RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48REFor Exercises 49-52, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. log100c2+1050REFor Exercises 49-52, write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. lnab23cd552REFor Exercises 53-55, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. 4log5y3log5x+12log5zFor Exercises 53-55, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. log250+log2log555RE56REFor Exercises 56-58, use logb20.289,logb30.458,andlogb50.671 to approximate the value of the given logarithms. logb45For Exercises 56-58, use logb20.289,logb30.458,andlogb50.671 to approximate the value of the given logarithms. logb1959RE60RE61REFor Exercises 61-80, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 10002x+1=1100x4For Exercises 61-80, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 7x=51For Exercises 61-80, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 516=11w21For Exercises 61-80, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 32x+1=43xFor Exercises 61-80, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 2c+3=72c+5For Exercises 61-80, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 400e2t=2.98968RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82REThe percentage of visible light P (in decimal form) at a depth of x meters for Long Island Sound can be approximated by P=e0.5x. a. Determine the depth at which the light intensity is half the value from the surface. Round to the nearest hundredth of a meter. Based on your answer, would you say that Long Island Sound is murky or clear water? b. Determine the euphotic depth for Long Island Sound. That is, find the depth at which the light intensity falls below 1. Round to the nearest tenth of a meter.For Exercises 84-85, solve for the indicated variable. logB1.7=2.3MforBFor Exercises 84-85, solve for the indicated variable. T=Tf+T0ektfort86RE87RE88RE89RE90RE91REGiven fx=4x31, a. Write an equation for f1x. b. Verify that ff1x=f1fx=x.2T3TFor Exercises 4-7, a. Write the domain and range of f in interval notation. b. Write an equation of the inverse function. c. Write the domain and range of f1 in interval notation. fx=x2+1,x05TFor Exercises 4-7, a. Write the domain and range of f in interval notation. b. Write an equation of the inverse function. c. Write the domain and range of f1 in interval notation. fx=3x+1For Exercises 4-7, a. Write the domain and range of f in interval notation. b. Write an equation of the inverse function. c. Write the domain and range of f1 in interval notation. fx=x+5For Exercises 8-11, a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. d. Write an equation of the asymptote. fx=13x+2For Exercises 8-11, a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. d. Write an equation of the asymptote. gx=2x4For Exercises 8-11, a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. d. Write an equation of the asymptote. hx=lnxFor Exercises 8-11, a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. d. Write an equation of the asymptote. kx=log2x+13Write the statement in exponential form. lnx+y=a13T14TFor Exercises 13-18, evaluate the logarithmic expression without using a calculator. lne816T17T18T19T20T21T22TFor Exercises 23-24, write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. 6log2a4log2b+23log2c24T25T26T27T28T29T30T31T32TFor Exercises 27-36, solve the equation. Write the solution set with exact values and give approximate solutions to 4 decimal places. 5lnx+2+1=1634T35T36T37TFor Exercises 37-38, solve for the indicated variable. A=P1+rnntfortSuppose that $10,000 is invested and the account grows to $13,566.25 in 5 yr. a. Use the model A=Pert to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. b. Using the interest rate from part (a), how long will it take the investment to reach $50,000? Round to the nearest tenth of a year.40TThe population Pt of a herd of deer on an island can be modeled by Pt=12001+2e0.12t, where t represents the number of years since the park service has been tracking the herd. a. Evaluate P0 and interpret its meaning in the context of this problem. b. Use the function to predict the deer population after 4 yr. Round to the nearest whole unit. c. Use the function to predict the deer population after 8 yr. d. Determine the number of years required for the deer population to reach 900. Round to the nearest year. e. What value will the term 2e0.12t approach as t? f. Determine the limiting value of Pt.The number N of visitors to a new website is given in the table t weeks after the website was launched. a. Use a graphing utility to find an equation of the form N=abt to model the data. Round ato1 decimal place and bto3 decimal places. b. Use a graphing utility to graph the data and the model from part (a). c. Use the model to predict the number of visitors to the website 10 weeks after launch. Round to the nearest thousand.1CREFor Exercises 1-2, simplify the expression. 52x233CRE4CREFor Exercises 5-13, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. 53+2x76CRE7CRE8CRE9CRE10CRE11CRE12CRE13CRE14CRE15CRE16CREGiven fx=3x+6x2, a. Write an equation of the vertical asymptote(s). b. Write an equation of the horizontal or slant asymptote. c. Graph the function.18CRE19CRE20CREDetermine whether the function is one-to-one. a.h=4,5,6,1,2,4,0,3b.k=1,0,3,0,4,5Use the horizontal line test to determine if the graph defines y as a one-to-one function of x.Determine whether the function is one-to-one. a.fx=4x+1b.fx=x3
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