978-0538449670 Chapter 5 Workbook Solutions

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Exercises

Classified Ads

1. Enrique plans to sell his car and places a 6-line ad. His paper charges $42 for the  rst two

lines and $6.75 per extra line, to run the ad for one week. What will Enrique’s ad cost to run

for three weeks?

7. Dr. Mandel purchased a used car for $11,325. Her state charges 8% tax for the car, $53 for

license plates, and $40 for a state safety and emissions inspection. How much does she need

to pay for these extra charges, not including the price of the car?

5-1

$999

or duplicated, or posted to a publicly accessible website, in whole or in part.

Financial Algebra Workbook 5-4

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7. Mrs. Lennon has 100/275/50 liability insurance and $50,000 PIP insurance. During an ice

storm, she hits a fence and bounces into a store front with 11 people inside. Some are hurt

and sue her. A passenger in Mrs. Lennon’s car is also hurt.

a. The store front will cost $24,000 to replace. There was $1,450 worth of damage to the

fence. What insurance will cover this, and how much will the company pay?

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11. The straight line depreciation equation for a truck is y = –4,265x + 59,710.

a. What is the original price of the car?

c. Suppose that T represents a length of time in years when the car still has value. Write an

algebraic expression to represent the value of the car after T years.

d. Suppose that after a years, the car depreciates to b dollars. Write an algebraic

expression for a.

–2,682x + 32,814

b – 32,814

________

–2,682

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14. The graph of a straight line depreciation equation is shown.

$19,200

14

years

value

0

$12,800

$3,200

246

$6,400

$9,600

$16,000

8 10 12

a. Use the graph to approximate the value of the car after 4 years.

b. Use the graph to approximate the value of the car after 5 years.

c. Use the graph to approximate when the car will be worth half its original value.

15. Tom purchased a new car for $36,000. He has determined that it straight line depreciates

over 12 years. When he purchased the car, he made a $6,000 down payment and  nanced

the rest with a  ve-year loan where he pays $610 per month.

a. Create an expense and depreciation function where x represents the number of months.

b. After how many months will the amount invested in the car be equal to the value of the

car? Round your answer to the nearest month.

$12,800

$11,200

6 years

Depreciation: y = –250x + 36,000; Expense: y = 610x + 6,000

35 months

Exercises

1. Tanya’s new car sold for $23,856. Her online research indicates that the car will depreciate

exponentially at a rate of 6

3

__

8

% per year. Write the exponential depreciation formula for

Tanya’s car.

2. The screen to the right is from a graphing calculator after running an

exponential regression analysis of a set of automobile data. X represents

years and y represents car value. Using the numbers on the screen,

write the exponential regression equation.

8. A car exponentially depreciates at a rate of 8.5% per year. Mia purchased a 4-year-old car for

$17,500. What was the original price of the car when it was new? Round your answer to the

nearest thousand dollars.

9. Nancy and Bob bought a used car for $22,800. When this car was new, it sold for $30,000. If

the car depreciates exponentially at a rate of 9.2% per year, approximately how old is the car?

Round your answer to the nearest hundredth of a year.

Historical and Exponential

Depreciation

5-6

y=a*b^x

a=43754.00259

ExpReg

b=.8223288103

1 –

(

A

__

C

)

$25,000

2.84 years

y = 23,856(1 – 0.06375)x

B

Name _____________________________________________________________ Date ________________________

10. A car originally sold for $21,000. It depreciates exponentially at a rate of 6.2% per year. When

purchasing the car, Jon put $5,000 down and pays $3,000 per year to pay o the balance.

a. Write the exponential depreciation equation. Write the expense equation.

Name _____________________________________________________________ Date ________________________

9. Complete the table. Round entries to the nearest hundredth.

Distance

(mi)

Rate

(mph)

Time

(hours) MPG Gallons

Used

Price per

gallon ($)

Cost for

Fuel ($)

10. Monique is away at college, and needs something from home, 625 miles away. She arranges

to meet her father at a location in between home and college, so he can drop o the item.

a. Monique averages 55 mph, and her part of the trip takes h hours. Represent the miles she

covered algebraically.

b. Her father takes 2 more hours than Monique to make his part of the trip, and his average

speed is 50 mph. Represent the distance he covered algebraically.

c. What is the sum of the distances they covered, expressed algebraically, using your

answers from parts a and b?

d. What is the sum of the distances they covered?

e. Write an equation that can be used to  nd the number of hours they traveled.

f. How many hours did it take Monique to do her part of the trip?

h. How many hours did it take her father to do his part of the trip? How many miles did her

father drive?

11. Francois’ car gets about 12.5 kilometers per liter. He is planning a 1,600-kilometer trip.

a. About how many liters of gas should Francois plan to buy? Round your answer to the

nearest liter.

12. Ace Car Rental charges customers $0.18 per mile driven. You picked up a car and the

odometer read x miles and brought it back with the odometer reading y miles. Write an

algebraic expression for the total cost Ace would charge you for mileage use on a rented car.

r

x

55h

50(h + 2)

105h + 100

625 miles

105h + 100 = 625

5

7; 350

128

$151.04

$0.18(y – x)

275