Question

Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. y=a(1/2)^t

Exponential growth and decay
ANSWERED
asked 2021-06-27
Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent.
\(\displaystyle{y}={a}{\left(\frac{{1}}{{2}}\right)}^{{t}}\)

Answers (1)

2021-06-28

\(\displaystyle{y}={a}{\left(\frac{{1}}{{2}}\right)}^{{t}}\)
This is a decay function
Rate of decay is \(1-0.5=0.5\)
That is 50%
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 \(1-a\)

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