Question

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

Probability and combinatorics
ANSWERED
asked 2021-06-08

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

Answers (1)

2021-06-09

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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