Section P.1 Homework

1.  Use the model given to answer the question about the object or process being modeled.  The volume V of a cylindrical can is modeled by the formula

V = 𝜋r²h

where r is the radius and h is the height of the can. Find the volume of a can with radius r = 2 in.  and height h = 4 in.  (Round your answer to one decimal place.)

____

2.   Use the model given to answer the questions about the object or process being modeled.   The gas mileage M (in mi/gal) of a car is modeled by M = N/G,  where N is the number of miles driven and G is the number of gallons of gas used.

(a) Find the gas mileage M for a car that drove 252 mi on 7 gal of gas.

(b) A car with a gas mileage M = 27 mi/gal  is driven 243 mi. How many gallons of gas are used?

3.  Use the model given to answer the questions about the object or process being modeled.  A mountain climber models the temperature T (in °F) at elevation h (in ft) by T = 54 − 0.005h.

(a) Find the temperature T at an elevation of 1100 ft.

(b) If the temperature is 47°F, what is the elevation?

4.   Use the model given to answer the questions about the object or process being modeled.  The power P measured in horsepower (hp) needed to drive a certain ship at a speed of s knots is modeled by P = 0.02s³.

(a) Find the power needed to drive the ship at 19 knots.

(b) At what speed will a 2.5-hp engine drive the ship?

5.  Use the model given to answer the questions about the object or process being modeled.  Arizonans use an average of 46 gal of water per person each day. The number of gallons W of water used by x Arizonans each day is modeled by W = 46x.

(a) Make a table that gives the number of gallons of water used for each 1000-person change in population, from 0 to 5000.

(b) What is the population of an Arizona town whose water usage is 138,000 gal per day.

6.  Write an algebraic formula that models the given quantity.  The average A of two numbers a and b

7.  Write an algebraic formula that models the given quantity.  The distance d in miles that a car travels in t hours at 51 mi/h

8 At a certain car rental agency a compact car rents for $45 a day and 20¢ a mile.

(a) How much does it cost to rent a car for 4 days if the car is driven 270 mi?

(b) Find a formula that models the cost C (in dollars) of renting this car for n days if it is driven m miles.

(c) If the cost for a 4-day rental was $260, how many miles was the car driven?

9. Use the model given to answer the question about the object or process being modeled.  A bakery finds that the cost C (in dollars) of producing x apple pies is modeled by C = 50 + 1.25x.

Find the cost of producing 36 apple pies.

10. A phone card company charges a 30¢ connection fee for each call and 12¢ per minute.

(a) How much does a 22-minute call cost?

(b) Find a formula that models the cost C (in dollars) of a phone call that lasts t minutes.

(c) If a particular call costs $0.42, how many minutes did the call last?

(d) Find a formula that models the cost C (in cents) of a phone call that lasts t minutes if the connection fee is F cents and the rate is r cents per minute.