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: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. For sales functions, we want to find the average rate of change from $t = 0$ to $t=3$.

Step2: Calculate average rate of change for Product 1

For $g(t)=200(1.36)^{t}$, when $t = 0$, $g(0)=200(1.36)^{0}=200$. When $t = 3$, $g(3)=200(1.36)^{3}=200\times2.515456 = 503.0912$. The average rate of change of $g(t)$ from $t = 0$ to $t = 3$ is $\frac{g(3)-g(0)}{3 - 0}=\frac{503.0912 - 200}{3}=\frac{303.0912}{3}=101.0304$.

Step3: Calculate average rate of change for Product 2

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

Step4: Compare the average rates of change

Since $101.0304>91.33$, Product 1 has a greater average rate of increase in sales after three days.

Answer:

Product 1