Question

CONSIDER THE EXPONENTIAL FUNCTION F(x)=250(1.03)^x, which models shawnda’s savings account where x represents the number of years since the money way invested A GROWINGB DECAYING

Answer 1

$\text{The value in the parenthesis is greater than 1, so it is growing (option A)}$

Explanation:$\begin{gathered} \text{The given exponential function:} \\ f(x)=250(1.03)^x \\ \text{where x = number of years since the money was invested} \end{gathered}$

To determine if it is growing or decaying, we will compare the exponential function when it is growing with the given function

$\begin{gathered} \text{Exponential growth formula:} \\ f(x)=a(1+r)^x \\ \text{where a = initial value} \\ r\text{ = rate of growth} \\ x\text{ = number of years} \end{gathered}$$\begin{gathered} f(x)=250(1.03)^x \\ f(x)=250(1+0.03)^x \\ \text{if value in parenthesis is greater than 1, it is a growth} \\ \text{if value in parenthesis is less than 1, it is a decay} \\ \end{gathered}$$Since\text{ the value in the parenthesis is greater than 1, then it is growing (optino A)}$