Question

Use the properties of exponents to rewrite y=3e^-0.6t in the form y=a(1+r)^t or y=a(1-r)^t. Round the value or r to the nearest thousandth. Then find the percent rate of change to the nearest tenth of a percent.

Rewritten function:


The percent decrease is about___%

Answer 1

`y=3(1-0.451)^t`

The value of r is 0.451

The percentage decrease is about 45.1%

Explanation:

The given exponential function is
`y=3e^(-0.6t)`

Using the exponent rule,
`(x)^(ab)=(x^a)^b`

`y=3(e^(-0.6))^t`

Now the value of
`e^(-0.6)=0.5488`

Thus, we can rewrite the function as

`y=3(0.5488)^t`

Therefore, the function in form
`y=a(1-r)^t`

`y=3(1-0.451)^t`

The value of r is 0.451

The percentage decrease is about 0.451 ×100 = 45.1%