Question

Sterling Company is testing the popularity of two products in the first days following their release. The quantity sold for Product 1, t days after its initial release, is modeled by the following function.
g(t)=200(1.36)^t

The quantity sold for Product 2, t days after its initial release, is shown in the following table.

t 0 1 2 3 4 5
f(t) 250 320 410 524 671 859
Based on this information, which product had the greater average rate of increase in sales after three days?
A.Both had the same average rate of increase in .sales.
B.Product 1
C.This cannot be determined from the given information.
D.Product 2

Answer 1

You're trying to determine the average rate of change after three days

So for the first equation g(t)

what do you get when you plug in t = 0 and t = 3

Answer 2

so when you plug in 0

g(t)=200(1.36)^t
g(0) = 200(1.36)^0

g(0) = ??


and then when t = 3
g(t)=200(1.36)^t
g(3) = 200(1.36)^3

g(3) = ??

Answer 3

Once you get those two values, we would need to find the average rate of change (which is also known as the slope) between those two points

The two points would be (0, ??? whatever you calculated) and (3, ???)

Those two ??? are the values you calculated in the previous step

I'll throw in colors for you in the slope formula

\(\Large\text{Slope} = \dfrac{\color{green}{y_2} - \color{orange}{y_1}}{\color{cyan}{x_2}-\color{red}{x_1}}\)

where you have two points
\(\Large (\color{red}{x_1}, \color{orange}{y_1})\) and \(\Large (\color{cyan}{x_2}, \color{green}{y_2})\)

So your two points are

\((\color{red}{0}, \color{orange}{??})\) and \((\color{cyan}{3}, \color{green}{??})\)