Question

With an annual rate of inflation of 4.5% over the next years,the approximate cost C of goods or services during any year in the decade is given by

c(t) = p(1.045)t, 0 ≤ t ≤ 10

Where t is the time (in years) and p is the represent cost.The price of a base ball game ticket is presently $20.Estimate the price 10 years from now.

Answer 1

Explanation:

Let us consider the exponential function
`C(t)=P(1.045)^(t),0\leqt\leq10`

Here
`t` is the time and
`P` is the present cost

Also, given the present cost is $20

Now to estimate the price 10 years from now,

Substitute
`t=10` and
`P=$20` in
`C(t)=(1.045)^t`

`C(t)=(1.045)^t\\=$20(1.045)^(10)\\=$31.06`

Therefore, price for the ticket is $31.06