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
Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent.
$$\displaystyle{y}={a}{\left(\frac{{1}}{{2}}\right)}^{{t}}$$

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 $$1-a$$