Question

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

Answer 1

ANSWER:

$\begin{gathered} y\approx a(1-0.06)^t \\ \\ \text{ The rate is about 6\% } \\ \\ \text{ It is a decay rate} \end{gathered}$

STEP-BY-STEP EXPLANATION:

We have the following expression:

$y=a\left(0.5\right)^{\frac{t}{12}}$

We rewrite a to the form desired by the statement as follows:

$\begin{gathered} y=a(1\pm r)^t \\ \\ \text{ In order to achieve this we do the following:} \\ \\ y=a(0.5)^{\frac{t}{12}}=\left(\left(0.5\right)^{\frac{1}{12}}\right)^t \\ \\ y=a(0.94)^t \\ \\ y=a(1-0.06)^t \\ \\ r=6\% \\ \\ \text{ The minus sign indicates that it is decay rate} \end{gathered}$