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2021-06-08

Suppose that f is an exponential function with percentage growth rate of 5% and that $f\left(0\right)=4$. Find a formula for f(x).

SchepperJ

Use the exponential equation:
$f\left(x\right)=a{\left(1+r\right)}^{x}$
where aa is the initial value and rr is the growth rate/decay.
Given $f\left(0\right)=4$, then $a=4$. Since we are given a growth rate, then $r=0.05$: $f\left(x\right)=4{\left(1+0.05\right)}^{x}$
$f\left(x\right)=4{\left(1.05\right)}^{x}$

Jeffrey Jordon