Question

If the rate of inflation is 3.9% 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)= 2500(1.039^t). find the current price of the item and the price 10 years from today. round your answers to the nearest dollar as necessary.

Answer 1

The current price of the item is $2500 and the price 10 years from today is $3665. 2.

Given exponential function

p(t) = 2500 × (1.039)^t

where t is the number of years from today.

Rate of inflation is 3.9% per year

The computation of the current price of the item and the price 10 years from today is shown below:-

p(t) = 2500 × (1.039)^t

Now, the current price can be found by putting t = 0

p(0) is

p(0) = $2500 \times (1.039)^{0}$

= 2500

The price 10 years from today can be found by putting t = 10

p(10) is

p(10) = $2500 \times (1.039)^{10}$

= 2500 × 1.466

= 3,665.181

Rounding to nearest dollar

= $3665. 2

The current price of the item is $2500 and the price 10 years from today is $3665. 2.

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