Question

If the rate of inflation is 1.9% per year, the future price pt (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.=pt8001.019t

Answer 1

Solution

- The formula given is

$\begin{gathered} p(t)=800(1.019)^t \\ where, \\ t=\text{ The number of years from today} \end{gathered}$

Price for today:

- The number of years from today is 0 years. Implying that

$t=0$

- Thus, we can find the price for today as follows:

$\begin{gathered} p(0)=800(1.019)^0 \\ p(0)=800\times1 \\ \\ \therefore p(0)=800 \end{gathered}$

- The cost today is 800

Price 9 years from today:

- The number of years from today is 9 years. Implying that

$t=0$

- Thus, we can find the price 9 years from now as follows:

$\begin{gathered} p(9)=800(1.019)^9 \\ p(9)=947.67 \end{gathered}$

- The cost 9 years from now is 947.67