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Average Rate of Change of a Function In Exercises 61-64, find the average rate of change of the function from
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College Algebra Real Mathematics Real People Edition 7
- Fuel Cost A car is driven 15,000 miles a year and getsx miles per gallon. Assume that the average fuel cost is$3.48 per gallon. Find the annual cost of fuel C as a functionof x and use this function to complete the table. Who would benefit more from a one-mile-per-gallon increase infuel efficiency—the driver of a car that gets 15 miles per gallonor the driver of a car that gets 35 miles per gallon? Explain.arrow_forwardThe millage rate is the amount of property tax per $1000 of the taxable value of a home. For a certain county the millage rate is 18 mil ($18 in tax per $1000 of taxable value of the home). A city within the county also imposes a flat fee of $108 per home. Part: 0 / 3 Part 1 of 3 (a) Write a function representing the total amount of property tax 7 (x) (in $) for a home with a taxable value of x thousand dollars. T (x) Part: 1/3 Part 2 of 3 = (b) Write an equation for T¹(x). -1 T¹(x) Part: 2 / 3 Part 3 of 3 x 00 X (c) Evaluate T¹(2736) and interpret its meaning in context. T¹(2736) = means that if a homeowner is charged $ in property taxes, then the taxable value of the home is Xarrow_forwardExercise refer to the functionarrow_forward
- Boyle's Law 2 states that for a certain container we have P · V = 345 where P represents gas in a the pressure of the gas (in mmHG) and V represents the volume of the gas (in liters). a. If the pressure of the gas is 225 mmHG, what is the volume of the gas? liters Preview b. Write a function f that determines the volume of the gas (in liters) in terms of the pressure of the gas in mmHG, P. f(P) Preview c. Complete the following statement. (Hint: if f(P) increases without bound, enter "oo". If f(P) decreases without bound, enter "-oo".) As P → 0*, f(P) → Previewarrow_forwardHow to know if y is a function of x.arrow_forwardDistance between cars At noon, car A is 10 feet to the right and 20 feet ahead of car B, as shown in the figure. If car A continues at 88 ft/sec (or 60 mi/hr) while car B continues at 66 f/sec (or 45 mi/hr), express the distance d between the cars as a function of t, where t denotes the number of sec- onds after noon. Exercise 78arrow_forward
- Pipe is to be laid from point A in a rectangular plot of size 10 x 20 feet to a point P on side BC and from there on to C as shown in red in the figure below. The cost of laying pipe within the plot is $c per foot (it must be underground), while the cost of laying pipe along the side of the plot is $d per foot. 10 A 20 (a) Determine the total cost, f(x), as a function of c, d and x, where x is the distance from P to B. (Note that f(x) is discontinuous at x = 0.) f(x) = dollars (b) What is the cost of laying the pipe on the side of the plot (x = 0) when c = 30 and d = 25? (Round your answer to the nearest cent.) (c) What is the least cost of laying the pipe when c = 30 and d = 25? (Round your answer to the nearest cent.)arrow_forwardWorld grain production was 1,241 million tons in 1975 and 2,048 million tons in 2005, and has been increasing at an approximately constant rate. (a) Find a linear function for world grain production, P, in million tons, as a function of t, the number of years since 1975.arrow_forwardDefine the term One-to-One Functions?arrow_forward
- What is the input value in a function?arrow_forwardA function is graphed below. On which interval of x is the average rate of change of the function the smallest? (69, 134) K 80 (38,76) 60 (25, 46) (9,24) 50 y 160 140 120 100 40 20 O (7,6) 10 20 x = 7 to x = 9 x = 25 to x = 38 30 40 60 70 x = 9 to x = 25 x = 38 to x = 69 80 Submit Answerarrow_forwardBoyle's Law 2 states that for a certain gas in a container we have P. V = 350 where P represents the pressure of the gas (in mmHG) and V represents the volume of the gas (in liters). a. If the pressure of the gas is 240 mmHG, what is the volume of the gas? liters Preview b. Write a function f that determines the volume of the gas (in liters) in terms of the pressure of the gas in mmHG, P. f(P) Preview c. Complete the following statement. (Hint: if f(P) increases without bound, enter "oo". If f(P) decreases without bound, enter "- o0".) As P → 0*, f(P) → Previewarrow_forward
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