[tex]\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}[/tex]
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
