Struggling with this problem

Question

Use the properties of exponents to rewrite y=5e^{-0.7t} in the form y=a(1+r)^t or y=a(1-r)^t . Round the value of r to the nearest thousandth. Then find the percent rate of change to the nearest tenth of percent.

Answer 1

Since x^ab = (x^a)^b we can rewrite the function:

y = 5e^-0.7t = 5(e^-0.7)^t

e^-0.7 = 1 - 0.503

So:

y = 5e^-0.7t = 5(1-0.503)^t

The value loses 50.3% per period.