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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.

Rewrite y a05t12 in the form y a1rt or y a1rt Round each value to the nearest hundredth if necessary Then state the growth or decay rateThe rate is about It is class=

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ANSWER :

[tex]y=a(1-0.5)^{\frac{t}{12}}[/tex]

The rate is about -50%

It is a decay rate

EXPLANATION :

From the problem, we have :

[tex]y=a(0.5)^{\frac{t}{12}}[/tex]

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

[tex]\begin{gathered} 1+r=0.5 \\ r=0.5-1 \\ r=-0.5 \end{gathered}[/tex]

r is negative so the equation will be :

[tex]y=a(1-0.5)^{\frac{t}{12}}[/tex]

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.

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