If the rate of inflation is \( 2.6 \% \) 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. \[ p(t)=2500(1.026)^{t} \] Find the current price of the item and the price 10 years from today. Round your answers to the nearest dollar as necessary. Current price: Price 10 years from today: \( \$ \square \)

The current price of the item is given directly by the initial value in the exponential function. Thus, the current price is \( p(0) = 2500(1.026)^{0} = 2500 \). To find the price 10 years from today, substitute \( t = 10 \) into the function: \[ p(10) = 2500(1.026)^{10} \approx 2500 \times 1.28008 \approx 3200.20 \] Rounding to the nearest dollar, the price 10 years from today is \( \$3200 \). Current price: \( \$2500 \) Price 10 years from today: \( \$3200 \)