Question

(a) The annual inflation rate is 3.1% per year. If a movie ticket costs $11.50 today, find a formula for P, the price of a movie ticket t years from today, assuming that movie tickets keep up with inflation. P = f(t) = (b) According to your formula, how much will a movie ticket cost in 25 years? _______

Answer 1

Given:

The annual inflation rate = 3.1% per year

The cost of the ticket today = $11.5

Part A:

We need to write the formula P the price of a movie ticket t years from today.

So,

the formula will be:

$\begin{gathered} r=3.1\%=0.031 \\ \\ P=f(t)=11.5\cdot(1+0.031)^t \end{gathered}$

Part B:

According to your formula, how much will a movie ticket cost in 25 years?

So, we will substitute with t = 25 into the f(t)

So,

When t = 25

$\begin{gathered} P=f(t)=11.50\cdot(1+0.031)^{25}=11.5\cdot1.031^{25}=11.5\cdot2.1452 \\ \\ P=24.67 \end{gathered}$

So, the cost of the ticket after 25 years = $24.67