23. A company purchases a new car for $25,000 for their employees to use. For ac

Question

23. A company purchases a new car for $25,000 for their employees to use. For accounting purposes, -/they decide to depreciate the value of the car by 14.5% each year. Using this method of depreciation, what is the value of the car after 2 years? What is the ratio of the car's value in one year compared to its value the previous year? Explain the meaning of the value of this ratio. Define a function that models the value of the car as a function of the number of years since the company purchased it. When will the value of the car be less than $1000? a. b. c. d.

Explanation / Answer

initial value of car = $ 25000

depreciates by 14.5% each year

a) value of car after 2 years

25000*.855 - .145 ( 25000*.855)

= $ 18275.625

b) ratio of cars value in one year compared to other = 21375 / 25000

= 1.17

c) function is

V(t) = 25000 ( 1 - .145 )^t

d) value of car be less than $ 1000

25000 ( 1 - .145 )^t < 1000

.855 ^t < 1/25

t = 20.54

value of var will be less than 1000 in 21 years

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