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.

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22-02-2020
Mathematics

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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.

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jchoubay1 jchoubay1 · Answer 1 · 2020-02-23T11:17:26+01:00

Answer:

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

The expression represents an exponential growth function.

Step-by-step explanation:

Given that [tex]y=5(14)^{\frac{t}{6}[/tex]

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

[tex]y=5(14)^{\frac{t}{6}[/tex]

[tex]=5((14)^{\frac{1}{6}})^t[/tex]

[tex]=5[1.5525]^t[/tex]

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

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

facundo3141592 facundo3141592 · Answer 2 · 2022-01-27T10:58:48+01:00

We want to rewrite our exponential equation, we will get:

[tex]y = 5*(1 + 0.552)^t[/tex]

Which is an exponential growth equation.

Rewriting the equation:

We start with:

[tex]y = 5*(14)^{t/6}[/tex]

We can rewrite it as:

[tex]y = 5*((14)^{1/6})^t = 5*(1.552)^t[/tex]

Now we just need to write the thing inside the parenthesis as "one plus something" so we get:

[tex]y = 5*(1 + 0.552)^t[/tex]

Now, because the base of the exponential part is larger than 1, as the value of t increases also does the value of y, which means that this equation is an exponential growth equation.

If you want to learn more about exponential equations, you can read:

https://brainly.com/question/11464095