Question

Assuming that the annual rate of inflation averages 3% over the next 10 years, the approximate costs C of goods or services during any year in that decade will be modeled by C(t)=P(1.03) where t is the time in years and P is the present cost. The price of an oil change for your car is presently $23.97. Estimate the price 10 years from now. (Round your answer to the nearest cent.)

a) $32.64
b) $37.21
c) $41.97
d) $46.92

Answer 1

To estimate the future cost of an oil change with a 3% annual inflation rate over 10 years, use the formula C(t)=P(1.03)^t with the present cost, P, of $23.97. The future cost is found to be approximately $32.19.

Step-by-step explanation:

To estimate the future cost of an oil change given a 3% annual rate of inflation, you can use the formula provided, C(t)=P(1.03)^t, where C(t) is the cost after t years, P is the present cost, and t is the number of years into the future.

The present cost of an oil change is $23.97. To find the cost 10 years from now, plug the values into the formula:

1. Identify the given values: P = $23.97, t = 10.
2. Plug the values into the inflation formula: C(10) = 23.97 * (1.03)^10.
3. Calculate the power of 1.03 raised to the 10th power.
4. Multiply this result by the current price of $23.97.

After performing the calculation:

C(10) = 23.97 * (1.03)^10 = 23.97 * 1.343916379 = $32.19 (rounded to the nearest cent).

Therefore, the estimated cost of an oil change 10 years from now is approximately $32.19.