Question

Which of the equations below represent exponential decay? Select all that apply. •y= (0.01)^x •y= 500(1-0.35)^x •y= (5.45)^x •y= (1/2)^x •y= (4/5) 3^x

Answer 1

Answer:
`\begin{gathered} y=(0.01)^x \\ \text{y = 500(1-0.35)}^x \\ y\text{ = (}(1)/(2))^x \end{gathered}`Explanations:

The exponential decay equation is of the form:

`y\text{ = a(}1-b)^x`

where a = the original amount

b = decay factor

x = time

For the equation to represent an exponential decay, 1-b must be less than 1. That is, b > 0

The options that represent this equation are:

`\begin{gathered} y=(0.01)^x \\ \text{y = 500(1-0.35)}^x \\ y\text{ = (}(1)/(2))^x \end{gathered}`