Question

Given the following exponential function, identify whether the change represents

growth or decay, and determine the percentage rate of increase or decrease.
y=3100(0.365)

Answer 1

the rate is usually the number in the parentheses in an exponential function, now the tell-tale piece is that, if the rate is less than 1, we have a Decay expression, and if the rate is more than 1, then is Growth.

well, let's see 0.365 is less than 1, so it's Decay.

`\qquad \textit{Amount for Exponential Decay} \\\\ y=P(1 - r)^t\qquad \begin{cases} y=\textit{current amount}\\ P=\textit{initial amount}\dotfill &3100\\ r=rate\to r\%\to (r)/(100)\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ y = 3100(\stackrel{\stackrel{0.365}{\downarrow }}{1-(r)/(100)})^t\qquad \textit{this means that }\qquad 1-\cfrac{r}{100}=0.365 \\\\\\ -\cfrac{r}{100}=-0.635\implies r=(-100)(-0.635)\implies r=\stackrel{\%}{63.5}`