If the rate of inflation is 2.5% 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.

Question

If the rate of inflation is 2.5% 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(1.025)^t

Find the current price of the item and the price 10 years from today.

Round your answers to the nearest dollar as necessary.

Answer 1

Hi Stefani,

In this equation, t is the number of years from today. So if we want to find the current price, t=0. So all we need to do is plug 0 in for t. This looks something like

p(t) = 2000(1.025)^t

p(0) = 2000(1.025)⁰

Remember that any number raised to the power of 0 will result in 1, so this simplifies to

p(0) = 2000 (1) = 2000

So the current price is $2000.

If we want to find the price 10 years from now, we set t =10, and our equation becomes

p(10) = 2000(1.025)¹⁰

p(10) = 2560

So the price 10 years from now, to the nearest dollar, will be $2560.

Hope this helps!