Question

Rewrite y = a(0.5)^t/12 in the form y = a(1+r)^t or y = a(1-r)^t. Round each value to the nearest hundredth, if necessary. Then state the growth or decay rate.The rate is about %.It is a growth rate.

Answer 1

`y=a(1-0.5)^{(t)/(12)}`

The rate is about -50%

It is a decay rate

EXPLANATION :

From the problem, we have :

`y=a(0.5)^{(t)/(12)}`

Equate the term inside the parenthesis to (1 + r)

`\begin{gathered} 1+r=0.5 \\ r=0.5-1 \\ r=-0.5 \end{gathered}`

r is negative so the equation will be :

`y=a(1-0.5)^{(t)/(12)}`

The rate is the variable r x 100 which is -0.5 x 100 = -50%

Since the sign of r is negative, it is a decay rate.