Question

With an annual rate of inflation of 1.5% over the next 10 years, the approximate cost C of goods or services during any year in the decade is given by C(t) = P(1.015)t, 0 ≤ t ≤ 10 where t is time (in years) and P is the present cost. The price of an oil change for a car is presently $23.05. Estimate the price 10 years from now. (Round your answer to two decimal places.)

Answer 1

- The equation of inflation over a 10 year period for all goods is given as:

`\begin{gathered} C(t)=P(1.015)^t \\ where, \\ 0\le t\le10 \end{gathered}`

- We are told that an oil change costs $23.05 now and we are asked to find the cost of an oil change in the next 10 years. This means that t = 10.

- Thus, we can simply substitute the value of t = 10 into the equation given to us and find the cost of an oil change 10 years later.

- This is done below:

`\begin{gathered} P=23.05 \\ t=10 \\ \\ \therefore C(10)=23.05(1.015)^(10) \\ C(10)=26.750466...\approx\$26.75\text{ \lparen To two decimal places\rparen} \end{gathered}`

Final Answer

The cost of an oil change 10 years later is $26.75