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

Answer:

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

The value of r is 0.451

The percentage decrease is about 45.1%

Step-by-step 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%