The value of a new 2022 Jeep Wrangler Rubicon was 67,035 when it went on the market. The value of the car deprecates at rate for 9.7% per year, Which function models the cars value, V, t years since 2022

A.V(t)=67035(0.097)^t
B.V(t)=67035(0.003)^t
C.V(t)=67035(0.903)^t
D.V(t)=67035(1.097)^t

1 answer

To model the value of a car that depreciates at a specific percentage per year, we typically use the formula:

\[ V(t) = V_0 \times (1 - r)^t \]

where:

  • \( V_0 \) is the initial value of the car,
  • \( r \) is the depreciation rate (expressed as a decimal),
  • \( t \) is the number of years since the car was purchased.

In this case, the initial value \( V_0 \) is 67,035, and the depreciation rate \( r \) is 9.7%, which is 0.097 in decimal form.

The formula for the value of the car after \( t \) years would become:

\[ V(t) = 67035 \times (1 - 0.097)^t \] \[ V(t) = 67035 \times (0.903)^t \]

Therefore, the correct answer is:

C. \( V(t) = 67035(0.903)^t \)