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

Given: Rate of inflation is 2.6% per year, p(t)=600(1.026)t

To find:  The current price of the item and the price 9 years from today.

Solution:

• So, we have given the rate of inflation as 2.6% per year.

• Now, the current price will be:

          p(t)=600(1.026)t

          at t = 0,

          p(0) = 600(1.026)^0

          p(0) = 600

• So the current price is dollars 600

• Now, for the price 9 years from today,we have t = 9.

         p(9) = 600(1.026)^9

         p(9) = 600 x 1.259871

         p(9) = 755.922 dollars

Answer:

                 The current price of the item and the price 9 years from today are dollar 600 and dollar 755.922 respectively.