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If the rate of inflation is 2.5% 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

If the rate of inflation is 25 per year the future price PT in dollars of a certain item can be modeled by the following exponential function where T is the num class=


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Solution:

The future price p(t), in dollars, can be modelled by the exponential function;

[tex]p(t)=800(1.025)^t[/tex]

(a) The current price is;

[tex]\begin{gathered} t=0; \\ \\ p(0)=800(1.025)^0 \\ \\ p(0)=800(1) \\ \\ p(0)=800 \end{gathered}[/tex]

ANSWER: $800

(b) The price 8 years from today;

[tex]\begin{gathered} t=8 \\ \\ p(8)=800(1.025)^8 \\ \\ p(8)=800(1.2184) \\ \\ p(8)=974.72 \\ \\ p(8)\approx975 \end{gathered}[/tex]

ANSWER: $975

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