Evaluating an exponential function that models a real-worid situation

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 $f$ is the number of years from today.
\[
p(t)=1200(1.025)^{t}
\]

Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
Current price:
Price 8 years from today: $5 \square$
Explanation
Check
Terms of Use
Privery center
Accessionity

Step 1 ：The question is asking for the current price of the item and the price 8 years from today. The current price can be found by substituting t=0 in the given function, because the current time is 0 years from today. The price 8 years from today can be found by substituting t=8 in the given function.

Step 2 ：Let's calculate the current price: \(p(0)=1200(1.025)^{0}\)

Step 3 ：So, the current price of the item is \(\boxed{1200}\) dollars

Step 4 ：Now, let's calculate the price 8 years from today: \(p(8)=1200(1.025)^{8}\)

Step 5 ：So, the price 8 years from today will be \(\boxed{1462}\) dollars

Step 6 ：Final Answer: The current price of the item is \(\boxed{1200}\) dollars and the price 8 years from today will be \(\boxed{1462}\) dollars.