Question

If the rate of inflation is 3.4% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.p(t)=2000(1.034)tFind the current price of the item and the price 10 years from today.Round your answers to the nearest dollar as necessary.

Answer 1

The current price can be found replacing t=0 in the function:

$\begin{gathered} p(t)=2000(1.034)^t \\ p(0)=2000(1.034)^0 \\ p(0)=2000 \end{gathered}$

Which is 2000.

Now, to find the price 10 years from today, what we do is to replace t=10 in the function given like this:

$\begin{gathered} p(t)=2000(1.034)^{10} \\ p(t)=2794.057 \end{gathered}$

Rounded to the nearest dollar, the result is 2794.