Question

What function has a percent rate of decrease equal to 5%

Answer 1

Exponential decay is when an original amount is reduced by a consistent rate over a period of time, is generally expressed in percent change.

Exponential functions are represented by:

$\begin{gathered} y=a(1-b)^x \\ \text{where,} \\ a=\text{original amount} \\ (1-b)=\text{decay factor or percent rate of decrease} \\ x=\text{represents time} \end{gathered}$

Then, a percent rate of decrease of 5% is equal to 0.05 in decimal form.

Therefore, the function that has this decay factor is:

$f(x)=3(0.05)^x$