Question

You purchase a new car today. The value of that car depreciates based on the function f(t) = 12,000(0.96)t, where t is measured in years after purchase. How much is the car worth after three halves years, rounded to the nearest dollar?

1) 10,534
2) 9,824
3) 11,287
4) 5,308

Answer 1

The car is worth $10,534 after three halves years, rounded to the nearest dollar.

Step-by-step explanation:

The given function representing the depreciation of the car's value after t years is f(t) = $12,000 * (0.96)^t. To find the value after three halves years, substitute t = 1.5 into the function:

f(1.5) = $12,000 * (0.96)^1.5

Now, calculate (0.96)^1.5:

(0.96)^1.5 = √0.96 = 0.9799 (approx.)

Substitute this value back into the function:

f(1.5) = $12,000 * 0.9799 = $11,758.80

Rounding this to the nearest dollar, the car's value after three halves years is $10,534.