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.
We want to rewrite our exponential equation, we will get:
[tex]y = 5*(1 + 0.552)^t[/tex]
Which is an exponential growth 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
