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

preprekomW 2021-10-06 Answered
Suppose that f is an exponential function with percentage growth rate of 5% and that f(0) = 4. Find a formula for f(x).

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## Expert Answer

unett
Answered 2021-10-07 Author has 11041 answers
Use the exponential equation:
$$\displaystyle{f{{\left({x}\right)}}}={a}{\left({1}+{r}\right)}^{{x}}$$
where aa is the initial value and rr is the growth rate/decay.
Given f(0)=4, then a=4. Since we are given a growth rate, then r=0.05: $$\displaystyle{f{{\left({x}\right)}}}={4}{\left({1}+{0.05}\right)}^{{x}}$$
$$\displaystyle{f{{\left({x}\right)}}}={4}{\left({1.05}\right)}^{{x}}$$

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