Question

Frances is selling glasses of lemonade. The function g(t) models the number of glasses she sold after t hours. What is the average rate at which she is selling lemonade between t = 2 and t = 6?

a) [Calculate the average rate]
b) There is not enough information to calculate the average rate.
c) The average rate is 0.
d) The average rate is 9.

Answer 1

To calculate the average rate at which Frances is selling lemonade between t = 2 and t = 6, we need to evaluate the function g(t) at both time points and calculate the rate of change. The average rate of change is (g(6) - g(2))/4.

Step-by-step explanation:

To calculate the average rate at which Frances is selling lemonade between t = 2 and t = 6, we need to evaluate the function g(t) at both time points and calculate the rate of change. The average rate of change is given by the formula: average rate = (g(6) - g(2))/(6 - 2). This can be simplified to (g(6) - g(2))/4. By plugging in the values of t=2 and t=6 into the function g(t), we can calculate the average rate at which Frances is selling lemonade.

Let's assume g(t) = 2t + 3. Plugging in t=2, we get g(2) = 2(2) + 3 = 7. Plugging in t=6, we get g(6) = 2(6) + 3 = 15. Therefore, the average rate at which Frances is selling lemonade between t = 2 and t = 6 is (15 - 7)/4 = 2 glasses per hour.