Question

Rewrite y=5(14)t/6 in the form y=a(1+r)t or y=a(1−r)t. Round the value of r to the nearest ten thousandth. Then tell whether the model represents exponential growth or exponential decay.

Answer 1

Answer:

$y=5(1+0.5525)^t$ where r=0.5525  which is in the form of $y=a(1+r)^t$ or $y=a(1-r)^t$..

The expression represents an exponential growth function.  

Step-by-step explanation:

Given that $y=5(14)^{\frac{t}{6}$

To rewrite the given equation in the form $y=a(1+r)^t$ or $y=a(1-r)^t$..

$y=5(14)^{\frac{t}{6}$

 $=5((14)^{\frac{1}{6}})^t$

$=5[1.5525]^t$

$y=5(1+0.5525)^t$ where r=0.5525  which is in the form of $y=a(1+r)^t$ or $y=a(1-r)^t$..

Since 1.5525 > 1, we have that the expression represents an exponential growth function.