Question

If the rate of inflation is 3.4%per year, the future price pt(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(1.034)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 is $3000 and price after 9 years from today is $4054.

Explanation:

The future price pt(in dollars) of a certain item can be modeled by the following exponential function

`p(t)=3000(1.034)^t`

where, t is the number of years from today.

Substitute t=0 to find the current price.

`p(0)=3000(1.034)^0=3000`

Therefore the current price is $3000.

Substitute t=9 to find the price after 9 years from today.

`p(9)=3000(1.034)^9`

`p(9)=3000(1.35109177087)`

`p(9)=4053.27531261`

`p(9)\approx 4054`

Therefore the price after 9 years from today is $4054.