A car was purchased for $25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function that will determine the value V (t), of the car t years after purchase. Determine to the nearest cent, how much the car will depreciate from year 3 to year 4

Question

Mathematics

Jazmin Harrison

19 March, 18:26

A car was purchased for $25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function that will determine the value V (t), of the car t years after purchase. Determine to the nearest cent, how much the car will depreciate from year 3 to year 4

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Mariana Best · Answer 1

V (t) = 25000 * (0.815) ^t

The depreciation from year 3 to year 4 was $2503.71

Step-by-step explanation:

We can model V (t) as an exponencial function:

V (t) = Vo * (1+r) ^t

Where Vo is the inicial value of the car, r is the depreciation rate and t is the amount of years.

We have that Vo = 25000, r = - 18.5% = - 0.185, so:

V (t) = 25000 * (1-0.185) ^t

V (t) = 25000 * (0.815) ^t

In year 3, we have:

V (3) = 25000 * (0.815) ^3 = 13533.58

In year 4, we have:

V (4) = 25000 * (0.815) ^4 = 11029.87

The depreciation from year 3 to year 4 was:

V (3) - V (4) = 13533.58 - 11029.87 = $2503.71