Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. y=a(5/4)^t

Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. y=a(5/4)^t

Question
Exponential growth and decay
asked 2021-03-11
Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. \(\displaystyle{y}={a}{\left(\frac{{5}}{{4}}\right)}^{{t}}\)

Answers (1)

2021-03-12
\(\displaystyle{y}={a}{\left(\frac{{5}}{{4}}\right)}^{{t}}={a}{\left({1.25}\right)}^{{t}}\)
This is a growth function
Rate of decay is 1.25-1=0.25
That is 25%
Consider an exponential function of the form: \(\displaystyle{y}={b}\cdot{a}^{{x}}\)
If a>1, then it is exponential growth function with growth rate a-1
If a<1, then it is exponential decay function with decay rate 1-a
0

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