Question

If the rate of inflation is 2.5% 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)=1500(1.025)t
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.

Answer 1

SOLUTION

GIVEN

If the rate of inflation is 2.5% 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.

$\sf{p(t) = 1500 \times {(1.025)}^{t} }$

TO DETERMINE

The current price of the item and the price 8 years from today. Round to the nearest dollar as necessary.

EVALUATION

Here it is given that the rate of inflation is 2.5% per yea

If current price = P

Then the future price pt (in dollars) of a certain item can be modelled by the following exponential function, where t is the number of years from today as

$\displaystyle \: \sf{p(t) = P \times { \bigg(1 + \frac{2.5}{100} \bigg)}^{t} }$

$\implies \displaystyle \: \sf{p(t) = P \times { \bigg(1 + 0.025 \bigg)}^{t} }$

$\implies \displaystyle \: \sf{p(t) = P \times { \bigg(1 .025 \bigg)}^{t} }$

Now Comparing with

$\sf{p(t) = 1500 \times {(1.025)}^{t} }$

We get

Current price = P = $ 1500

After 8 years the price will be

$\sf{p(8) = 1500 \times {(1.025)}^{8} }$

= $ ( 1500 × 1.2184 )

= $ 1827.6

= $ 1828 ( Approx to the nearest dollar )

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