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 …

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asked Apr 27, 2023 105k views

1 Answer

Jackxujh · Answer 1 · 2023-05-02T11:58:14+0000

ANSWER :

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

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.