Question

If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where it is the

number of years from today.
P (0)=1200 (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 from 8 years from today$?

Answer 1

Answer: the price of the item 8 years from today is approximately $1475.

Explanation:

The given exponential function to model the future price of the item is:

P(t) = P(0) * (1.026)^t

Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.

1. To find the current price, we need to find P(0):

P(0) = 1200 * (1.026)^0

Since any number raised to the power of 0 is 1:

P(0) = 1200 * 1

P(0) = $1200

So, the current price of the item is $1200.

2. To find the price 8 years from today, we need to find P(8):

P(8) = 1200 * (1.026)^8

Using a calculator:

P(8) ≈ 1200 * 1.229057

P(8) ≈ $1474.87

Rounded to the nearest dollar:

P(8) ≈ $1475

So, the price of the item 8 years from today is approximately $1475.