If the rate of inflation is 3.7% per year, the furture 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

p (t) = 800 (1.037)^(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: $_

Answer 1

To find the current price of the item, we can plug \( t = 0 \) into the function \( p(t) = 800(1.037)^t \).

Current Price:

\[ p(0) = 800(1.037)^0 = 800(1) = 800 \] So, the current price of the item is $800.

Price 10 Years from Today:

Now, we will find the price 10 years from today by plugging \( t = 10 \) into the function.

\[ p(10) = 800(1.037)^{10} \]

Calculating \( 1.037^{10} \): \[ 1.037^{10} \approx 1.4107 \]

Now, calculate \( p(10) \): \[ p(10) \approx 800 \times 1.4107 \approx 1128.56 \]

Rounding to the nearest dollar: \[ p(10) \approx 1129 \]

Final Answers:

• Current price: $800
• Price 10 years from today: $1129