Rewrite r(t)=(0.88)^4t in the form y=a(1+r)^t or y=a(1−r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.
To rewrite the equation in one of the suggested forms, we first need to manipulate it to isolate the base.
Given: r(t) = (0.88)^4t
We start by noticing that (0.88)^4t can be expressed as [(0.88)^4]^t.
So, r(t) = [(0.88)^4]^t
Now, let's evaluate (0.88)^4 to a more precise decimal:
(0.88)^4 ≈ 0.5997
After rounding to the nearest hundredth, (0.88)^4 ≈ 0.60
Substituting this result back into the equation, we get:
r(t) = (0.60)^t
Now, we can rewrite this in the desired form:
r(t) = (1 - 0.40)^t
Rounding 0.40 to the nearest hundredth gives 0.40, so we have:
r(t) ≈ (1 - 0.40)^t
Comparing this form to the suggested forms, we can conclude that the equation represents exponential decay.