Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Note Some of the formulas below use the special number
12. A Car That Gets 32 Miles per Gallon The cost C of operating a certain car that gets 32 miles per gallon is a function of the price g, in dollars per gallon, of gasoline and the distance d, in miles, that you drive. The formula for
a. Use functional notation to express the cost of operation if gasoline costs 98 cents per gallon and you drive 230 miles. Calculate the cost.
b. Calculate
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FUNCTIONS AND CHANGE COMBO
- Medical Drugs When a certain medical drug is administered to a patient, the number of milligrams remaining in the patients bloodstream after t hours is modeled by D(t)=50e0.2t How many milligrams of the drug remain in the patients bloodstream after 3 hours?arrow_forwardPower Consumption: The figure shows the power consumption in San Francisco for a day in September (P is measured in megawatts; t is hours stating at midnight). (a) What was the power consumption at 6:00 A.M? At 6:00 P.m.? (b) When was the power consumption the lowest? (c) Find the net change in the power consumption from 9:00 A.M. to 7:00 P.M/arrow_forwardA Mathematical Term: If f=f(x), then we use dfdx to denote the rate of change in f. What is the technical mathematical term for dfdx?arrow_forward
- Temperature Conversions In everyday experience, the measure of temperature most often used are Fahrenheit F and Celsius C. Recall that the relationship between them is given by F=1.8C+32. Physicists and chemists often use the Kelvin temperature scale. You can get kelvinsK from degrees Celsius by using K=C+273.15. a. Explain in practical terms what K30 means, and then calculate that value. b. Find a formula expressing the temperature C in degrees Celsius as a function of the temperature K in kelvins. c. Find a formula expressing the temperature F in degrees Fahrenheit as a function of the temperature K in kelvins. d. What is the temperature in degrees Fahrenheit of an object that is 310 kelvins?arrow_forwardm Miles per Gallon The cost of operating a car depends on the gas mileage in that your car gets, the cost x per gallon of gasoline, and the distance d that you drive. a. How much does it cost to drive 100 miles if your car gets 25 miles per gallon and gasoline costs 349 cents per gallon? b. Find a formula that gives the cost C as a function of m, g, and d be sure to state the units of each variable. c. Use functional notation to show the cost of driving a car that gets 28 miles per gallon a distance of 138 miles if gasoline costs 3.69 per gallon Use the formula from part b to calculate the cost.arrow_forwardFor the experimental can described in Example 8, write the surface area as a function of (a) the radius r and (b) the height h.arrow_forward
- Computer Virus The number V of computers infected by a virus increases according to the model Vt=100e4.6052t, where t is the time in hours. Find the number of computers infected after (a) 1 hour, (b) 1.5 hours, and (c) 2 hours.arrow_forwardThe function A(d) gives the pain level on a scale of 0 to 10 experienced by a patient with d milligrams of a pain- reducing drug in her system.The milligrams of the drug in the patient’s system after t minutes is modeled by m(t) . Which of the following would you do in order to determine when the patient will be at a pain level of 4? a. Evaluate A(m(4)) . b. Evaluate m(A(4)) . c. Solve A(m(t))=4 . d. Solve m(A(d))=4 .arrow_forwardFlood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forward
- What Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean. Grocery Bill If c(p,s,h) is the cost of buying p bags of potato chips, ssodas, and h hot dogs, use functional notation to express the cost of buying 2 bags of potato chips, 3 sodas, and 5 hot dogs.arrow_forwardNew Equation of Change? The tax liability T in dollars, for a company that has an initial tax liability of 6200 is dTdt=0.02T. Here, t is time in years. What would be the equation of change for the tax liability if the initial tax liability were 7000?arrow_forward
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