Question

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) = 3000 (1.026)
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:

Answer 1

The current price of the item is simply p(0) = 3000, since we are looking for the price at time t = 0 (the present).

To find the price 8 years from today, we need to evaluate p(8) using the given exponential function:

p(8) = 3000 (1.026)^8

Using a calculator, we get:

p(8) ≈ 3849.87

Rounding to the nearest dollar, we get:

Current Price: $3,000
Price 8 years from today: $3,850

Therefore, the current price of the item is $3,000, and the price 8 years from today is $3,850 (rounded to the nearest dollar).