select the correct answer.\nsterling company is testing the popularity of two products in the first days…

select the correct answer.\nsterling 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.\ng(t)=200(1.36)^t\nthe quantity sold for product 2, t days after its initial release, is shown in the following table.\n|t|0|1|2|3|4|5|\n|f(t)|250|320|410|524|671|859|\nbased on this information, which product had the greater average rate of increase in sales after three days?\nthis cannot be determined from the given information.\nproduct 2\nboth had the same average rate of increase in sales.\nproduct 1

select the correct answer.\nsterling 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.\ng(t)=200(1.36)^t\nthe quantity sold for product 2, t days after its initial release, is shown in the following table.\n|t|0|1|2|3|4|5|\n|f(t)|250|320|410|524|671|859|\nbased on this information, which product had the greater average rate of increase in sales after three days?\nthis cannot be determined from the given information.\nproduct 2\nboth had the same average rate of increase in sales.\nproduct 1

Answer

Explanation:

Step1: Calculate average rate for Product 1

The formula for average rate of change of a function $y = g(t)$ from $t = 0$ to $t = 3$ is $\frac{g(3)-g(0)}{3 - 0}$. First, find $g(0)$ and $g(3)$. For $g(t)=200(1.36)^{t}$, when $t = 0$, $g(0)=200(1.36)^{0}=200\times1 = 200$. When $t = 3$, $g(3)=200(1.36)^{3}=200\times2.515456 = 503.0912$. Then the average rate of change is $\frac{503.0912 - 200}{3}=\frac{303.0912}{3}=101.0304$.

Step2: Calculate average rate for Product 2

The formula for average rate of change of a function from $t = 0$ to $t = 3$ using the table values is $\frac{f(3)-f(0)}{3 - 0}$. From the table, $f(0)=250$ and $f(3)=524$. So the average rate of change is $\frac{524 - 250}{3}=\frac{274}{3}\approx91.33$.

Answer:

Product 1