Question

If the rate of inflation is 3.7% 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. =pt400( 1.037)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

well, for the current price today, let's see, not even one day has passed, to we don't have a "t" value that's greater than 0, so since today 0years and 0days and 0seconds have passed, t =0


`\bf p(t)=400(1.037)^0\implies p(t)=400\cdot 1\implies \boxed{p(t)=400}`

now, 8 years from now, well, 8 years would had passed by then, t = 8


`\bf p(t)=400(1.037)^8\implies p(t)\approx 400\cdot 1.3373037\implies \boxed{p(t)\approx 535}`

Answer 2

P (t)=400 (1.037)^t
The current price is 400

The price 8 years from today is
P (8)=400×(1.037)^(8)=534.9 round your answer to get 535