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

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

$$\displaystyle{f{{\left({x}\right)}}}={a}{\left({1}+{r}\right)}^{{x}}$$
Given $$f(0)=4$$, then $$a=4$$. Since we are given a growth rate, then $$r=0.05$$: $$\displaystyle{f{{\left({x}\right)}}}={4}{\left({1}+{0.05}\right)}^{{x}}$$
$$\displaystyle{f{{\left({x}\right)}}}={4}{\left({1.05}\right)}^{{x}}$$