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: \( \$ \square \)

**Step 1. Find the current price** The current price is given by \( p(0) \). Plug \( t = 0 \) into the equation: \[ p(0)=2500(1.026)^0=2500(1)=2500. \] Thus, the current price is \$2500. **Step 2. Find the price 10 years from today** The price 10 years from today is \( p(10) \). Substitute \( t = 10 \) into the function: \[ p(10)=2500(1.026)^{10}. \] Calculate \( (1.026)^{10} \): One way to do this is to use logarithms, noticing that \[ (1.026)^{10}=\exp(10\ln(1.026)). \] Approximating, we have \[ \ln(1.026) \approx 0.0257, \quad 10\ln(1.026) \approx 0.257, \] and \[ \exp(0.257) \approx 1.293. \] Thus, \[ p(10) \approx 2500 \times 1.293 \approx 3232.5. \] Rounding to the nearest dollar, \[ p(10) \approx 3233. \] **Final Answers** Current price: \$2500 Price 10 years from today: \$3233