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how do I do i find the exponential percent change

How Do I Do I Find The Exponential Percent Change class=

Sagot :

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

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

Then, the function is

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

The exponential change is, then

[tex]\frac{\sqrt[]{6}}{4}=0.61[/tex]

and, in percent, it is 61%

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