The number of students in a cafeteria is modeled by the function p that satisfies the logistic differential equation dp/dt = 1/2000 p(200-p), where t is the time in seconds and p(0) = 25. what is the greatest rate of change, in students per second, of the number of students in the cafeteria?

Maximum rate of change will be

at p = 100

Explanation:

As we know that rate of change in students per second is given by

here we need to find the greatest rate of change in the number of students

So in order to find the greatest value of the rate of students we have to put the differentiation of of the above function to be zero

so we have

by solving above equation we have

so maximum rate of students will be at the condition when p = 100

so the value of maximum rate will be

pretty sure it's false