Solution
- The equation of inflation over a 10 year period for all goods is given as:
[tex]\begin{gathered} C(t)=P(1.015)^t \\ where, \\ 0\le t\le10 \end{gathered}[/tex]- 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:
[tex]\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}[/tex]Final Answer
The cost of an oil change 10 years later is $26.75
