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

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