Question

if the rate of inflation is 2.2% 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) = 600(1.022)^t
find the current price of the item and the price 10 years from today.
round your answers to the nearest dollar as necessary.
current price: $
price 10 years from today: $

Explanation:

Step1: Find current price (t=0)

Substitute \( t = 0 \) into \( p(t)=600(1.022)^t \).
\( p(0)=600(1.022)^0 = 600\times1 = 600 \).

Step2: Find price at t=10

Substitute \( t = 10 \) into \( p(t)=600(1.022)^t \).
\( p(10)=600(1.022)^{10} \). Calculate \( (1.022)^{10}\approx1.24307 \), so \( p(10)\approx600\times1.24307\approx745.84 \), round to nearest dollar: 746.

Answer:

Current price: $\boldsymbol{600}$
Price 10 years from today: $\boldsymbol{746}$