Q:

Select "Growth" or "Decay" to classify each function.Function Growth Decayy=200(0.5)^2t y=1/2(2.5)^t/6 y=(0.65)^t/4 Which equation can be used to find the solution of (1/3)^d−5 = 81 ?A. −d−5=4B. d + 5 = 4C. d−5=4D. −d+5=4

Accepted Solution

A:
1. The growth rate equation has a general form of: y = A (r)^t The function is growth when r≥1, and it is a decay when r<1. Therefore: y=200(0.5)^2t                    --> Decay y=1/2(2.5)^t/6                  --> Growth y=(0.65)^t/4                       --> Decay   2. We rewrite the given equation (1/3)^d−5 = 81   Take the log of both sides: (d – 5) log(1/3) = log 81 d – 5 = log 81 / log(1/3) d – 5 = - 4   Multiply both sides by negative 1: - d + 5 = 4 So the answer is D