Question

if the rate of inflation is 3.7% 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) = 1500(1.037)^t find the current price of the item and the price 9 years from today. round your answers to the nearest dollar as necessary.
current price: $
price 9 years from today: $

Explanation:

Step1: Calculate current price (t=0)

Substitute $t=0$ into $p(t)$:
$p(0)=1500(1.037)^0 = 1500 \times 1 = 1500$

Step2: Calculate price at t=9

Substitute $t=9$ into $p(t)$:
$p(9)=1500(1.037)^9$
First compute $(1.037)^9 \approx 1.3984$, then $1500 \times 1.3984 = 2097.6$, rounded to nearest dollar is 2098.

Answer:

Current price: $\$1500$
Price 9 years from today: $\$2098$