Question

Select "Growth" or "Decay" to classify each function.

Function Growth Decay
y=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=4

B. d + 5 = 4

C. d−5=4

D. −d+5=4

Answer 1

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