Question

Determine whether the function represents exponential growth or exponential decay. f(x)=50(1.1)^3x

Exponential growth and decay
ANSWERED
asked 2021-05-17
Determine whether the function represents exponential growth or exponential decay.
\(\displaystyle{f{{\left({x}\right)}}}={50}{\left({1.1}\right)}^{{3}}{x}\)

Answers (1)

2021-05-18
Use the Power of a Power Rule to have:
\(\displaystyle{f{{\left({x}\right)}}}={50}\cdot{\left({1.1}^{{3}}\right)}^{{x}}\)
Evaluate the power to have:
\(\displaystyle{f{{\left({x}\right)}}}={50}\cdot{\left({1.331}^{{x}}\right)}\)
The base of the function is 1.331 which is greater than 1.
This means that the function involves an exponential growth.
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