Question

P(t) = 2000(1.019)

Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
A) Current price: X 5
B) Price 8 years from today: ? Check

Answer 1

The current price of the item is $2000, and the price 8 years from today, calculated using the exponential function and compounded annually, will be approximately $2325.

Step-by-step explanation:

The question asks to calculate the current price and the price 8 years from today of an item, given the exponential function p(t) = 2000(1.019)t, where t is the number of years since the current year.

To find the current price, we substitute t = 0 into the function because we are considering the current year:

p(0) = 2000(1.019)0 = 2000(1) = $2000

The current price of the item is $2000.

To find the price 8 years from today, we substitute t = 8 into the function:

p(8) = 2000(1.019)8 ≈ $2000 * 1.1626 ≈ $2325

Therefore, the price of the item 8 years from today will be about $2325, when rounded to the nearest dollar.