Question

How do I do i find the exponential percent change

Answer 1

To find the exponential change, we need to notice first that at time t=0 we have 200 mg, and it seems taht after two hours it drops to 75 mg. Then, the function is

`\begin{gathered} f(x)=200r^x \\ f(2)=75=200r^2 \\ r^2=(75)/(200) \\ r=\sqrt[]{(75)/(200)} \\ r=\frac{\sqrt[]{6}}{4} \end{gathered}`

Then, the function is

`f(x)=200(\frac{\sqrt[]{6}}{4})^x`

The exponential change is, then

`\frac{\sqrt[]{6}}{4}=0.61`

and, in percent, it is 61%