Solution Found!
Menu Value Theorem The population of a culture of cells
Chapter 4, Problem 25RE(choose chapter or problem)
Mean Value Theorem The population of a culture of cells grows according to the function \(P(t)=\frac{100 t}{t+1}\), where \(t \geq 0\) is measured in weeks.
a. What is the average rate of change in the population over the interval [0, 8]?
b. At what point of the interval [0, 8] is the instantaneous rate of change equal to the average rate of change?
Questions & Answers
QUESTION:
Mean Value Theorem The population of a culture of cells grows according to the function \(P(t)=\frac{100 t}{t+1}\), where \(t \geq 0\) is measured in weeks.
a. What is the average rate of change in the population over the interval [0, 8]?
b. At what point of the interval [0, 8] is the instantaneous rate of change equal to the average rate of change?
ANSWER:Step-by-step solution Step 1 In this problem, the population of a culture of cells is given as P(t) = t +1, we have to find the average rate of change in the population over the interval [0,8]and we also have to find at what point of interval [0,8] is the instantaneous rate of change equal to the average rate of change. To find the requirement, we will be using the mean value theorem Mean Value Theorem: It states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c such that f(b)f(a) f(c) = ba