Question

Rewrite y = a(0.25) ¹/⁹ in the form y = a(1+r)' or y = a(1-r). Then state the growth or decay rate.y=The rate is %.This is arate.

Answer 1

INFORMATION:

We have the next function

$y=a(0.25)^{\frac{t}{9}}$

We must rewrite it in the form y = a(1+r)^t or y = a(1-r)^t and state the growth or decay rate

STEP BY STEP EXPLANATION:

To rewrite the function:

1. Write the original function

$y=a(0.25)^{\frac{t}{9}}$

2. Use exponential properties

$y=a\lbrack(0.25)^{\frac{1}{9}}\rbrack^t$

3. Simplify

$y=a(0.86)^t$

4. Rewrite in form y = a(1-r)^t

$y=a(1-0.14)^t$

Finally, r = 0.14. That means that the rate is 14% and since we used the form y = a(1-r)^t, it is a decay rate.

ANSWER:

1.

$y=a(1-0.14)^t$

2. The rate is 14%

3. This is a decay rate.