Question

If the rate of inflation is 3.9% per year, the future price p(t) (in dollars) of a certain item can be modeled by the exponential functionp(t) = 400(1.039)^twhere t is the number of years from today.Find the current price of the item and the price 10 years from today.Round your answers to the nearest dollar as necessary.

Answer 1

Answer:

• $400

,

• $586

Explanation:

An exponential price growth function is of the form:

$\begin{gathered} P(t)=P_o(1+r)^t \\ \text{where }P_o\text{ is the current price.} \end{gathered}$

Given the function:

$p\mleft(t\mright)=400\mleft(1.039\mright)^t$

(a)The current price of the item =$400

(b)In 10 years time, the price of the item will be:

$\begin{gathered} p\mleft(t\mright)=400\mleft(1.039\mright)^{10} \\ =586.4 \\ \approx\ 586\text{ (to the nearest dollar)} \end{gathered}$

The price 10 years from today is $586.