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)=600(1.026)t
Find the current price of the item and the price 9 years from today.
Round your answers to the nearest dollar as necessary.

Answer 1

The current price of the item is $600.

The price of the item 9 years from today will be of $756.

Explanation:

Price of the item:

The price of the item, in dollars, after t years, is given by:

`p(t) = 600(1.026)^t`

Current price of the item

This is p(0). So

`p(0) = 600(1.026)^0 = 600`

The current price of the item is $600.

9 years from today.

This is p(9). So

`p(9) = 600(1.026)^9 = 756`

The price of the item 9 years from today will be of $756.