670 812 PM imathasrationalreasoningnet ATT LTE The value o

@ 67%.-0. + 8:12 PM imathas.rationalreasoning.net AT&T; LTE The value of a car depreciates each year. Suppose that you purchased a car for $22,000 and the value of the car depreciates by 10% each year a. Determine the following i. Initial value of the car: 22000 dollars Preview ii. 1-year growth factor: 1.1 Preview ii. 1-year percent change: -90 % Preview b. Define a function f that determines the value of the car in terms of the number of years since the car was purchased, r Preview c. Determine the value of the car 7 years after it was purchased. (You may round your answer to the nearest penny) Preview License Points possible: 1 Unlimited attempts Score on last attempt: 0.2. Score in gradebook: 0.2

Solution

initial value = 22000

depreciates by 10% each year

22000 - .10* 22000

function becomes

22000 ( 1 - .10 )^x

or

f(x) = 22000 ( 0.9)^x

the function has a decay factor of 0.9

1 year percentage change

22000 - 19800 / 22000 * 100

= 10%

b) function is

f(x) = 22000 (0.9)^x

c) value of car 7 years after it was purchased is

y = 22000 (0.9)^7

y = 10522.53

so value after 7 years was $ 10522.53