Question

Given an exponential function for compounding interest, A(x) = P(0.77)^x , what is the rate of change as a percentage?

Answer 1

An exponential function is expressed as

`\begin{gathered} y=a(1+r)^x--\text{ equation 1} \\ where \\ r\Rightarrow rate\text{ of change} \end{gathered}`

Given the exponential function:

`A(x)=P(0.77)^x---\text{ equation 2}`

By comparison, we have

`\begin{gathered} 0.77=1+r \\ add\text{ -1 to both sides,} \\ 0.77-1=-1+1+r \\ \Rightarrow r=-0.23 \\ In\text{ percentage, we have} \\ r=-23\% \end{gathered}`

Hence, the correct option is