Question

Determine whether the function represents exponential growth or decay identify the percent rate of change

Answer 1

$\bf \qquad \textit{Amount for Exponential change}\\\\ A=P(1\pm r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{starting amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed period}\\ \end{cases}$

now, the + is growth, and - is decay

well, let's see hmm "something" is increasing at a rate of say hmm 25%, r = 25% or 25/100 or 0.25

now, if we plug that in the equation, the amount is increasing the rate is positive, so we get A = P(1+0.25)ᵗ  or A = P(1.25)ᵗ

now, notice, the value in the parentheses, is "greater than 1", because the 0.25 got added

now, let's say something decreases by 25%, so we use a negative rate, thus  A = P(1 - 0.25)ᵗ  or A = P(0.75)ᵗ

notice again, the value inside the parentheses, is "less than 1"

anyhow, that's the tell-tale part of an exponential function