The manufacturer's suggested retail price (MSRP) for a particular car is $25,125, and it is expected to be worth $19,645 in 2 years. (a) Find a linear depreciation function for this car. (b) Estimate the value of the car 3 years from now. (c) At what rate is the car depreciating? (a) What is the linear depreciation function for this car? f(x) = (Simplify your answer. Do not include the $ symbol in your answer.) Please Answer a-b.

a. Depreciation function

F = (1-r)^t

b, $17,357

c. 11.6%

Step-by-step explanation:

a. Firstly, we are told to find the linear depreciation function. This means an equation that shows how the depreciation is playing out.

To get this, we shall go the exponential way;

Let F = future value of the car, P = Present value of the car, r = percentage of depreciation and t = time or number of years

So the depreciation function will be;

F = P(1 - r)^t

c. Let’s calculate the rate at which it is depreciating

According to our formula, F = $19,645 while P = $25,125 and t = 3

The depreciation function is;

F = P(1-r)^t

So substituting these values, we have;

19,645 = 25,125(1-r)^2

Divide both sides by 25,125

19645/25125 = (1-r)^2

(1-r)^2 = 0.782

Find the square root of both sides;

1-r = √0.782

1-r = 0.884

r = 1-0.884 = 0.116 which is same as 11.6%

b. We want to find the cost of the car in 3 years

We use the same depreciation function;

F = P(1-r)^t

where in this case F = ? , P = 25,125 , r = 0.116 and t = 3

Substituting these values, we have

F = 25125(1-0.116)^3

F = 25125(0.884)^3 = $17,357

300pi

step-by-step explanation: