When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by $$f(t) = 10 + (0.8t)\sin\left(\frac{t^3}{100}\right) \text{ for } 0 < t \leq 12$$ where $f(t)$ is measured in pounds per hour and $t$ is the number of hours after the store opened. After the store has been open for three hours, store employees add bananas to the display table at a rate modeled by $$g(t) = 3 + 2.4\ln\left(t^2 + 2t\right) \text{ for } 3 < t \leq 12$$ where $g(t)$ is measured in pounds per hour and $t$ is the number of hours after the store opened. (a) How many pounds of bananas are removed from the display table during the first 2 hours the store is open? (b) Find $f'(7)$. Using correct units, explain the meaning of $f'(7)$ in the context of the problem. (c) Is the number of pounds of bananas on the display table increasing or decreasing at time $t = 5$? Give a reason for your answer. (d) How many pounds of bananas are on the display table at time $t = 8$?
When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by
$$f(t) = 10 + (0.8t)\sin\left(\frac{t^3}{100}\right) \text{ for } 0 < t \leq 12$$
where $f(t)$ is measured in pounds per hour and $t$ is the number of hours after the store opened. After the store has been open for three hours, store employees add bananas to the display table at a rate modeled by
$$g(t) = 3 + 2.4\ln\left(t^2 + 2t\right) \text{ for } 3 < t \leq 12$$
where $g(t)$ is measured in pounds per hour and $t$ is the number of hours after the store opened.\\
(a) How many pounds of bananas are removed from the display table during the first 2 hours the store is open?\\
(b) Find $f'(7)$. Using correct units, explain the meaning of $f'(7)$ in the context of the problem.\\
(c) Is the number of pounds of bananas on the display table increasing or decreasing at time $t = 5$? Give a reason for your answer.\\
(d) How many pounds of bananas are on the display table at time $t = 8$?