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

Question

2 years ago

5

years after purchase. How much is the car worth after 3/2 years, rounded to the nearest dollar

1 answer:

Alex · Answer 1 · 2023-10-12T22:44:49+03:00

Considering the definition of exponential function, the value of the car is 11,287.25 dollars.

<h3>What is exponential function</h3>

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)= aˣ

Being a a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

<h3>What is the price of the car</h3>

In this case, 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.

After 3/2 years, the value of the car is calculated as:

f(3/2)=12,000× $0.96^{3/2}$

Solving:

Finally, the value of the car is 11,287.25 dollars.

Learn more with this similar problems:

#SPJ1