The population of a culture of cells after t days is approximated by P(t)=(1600)/(1+7e^(-0.02t)) when t ≥ 0 ?

A) Find the rate of change of the population of cells with respect to time

B) What is the instantaneous rate of change after 5 days?

1 Answer
Mar 23, 2018

a) The rate of change is simply the derivative with respect to time. We can find it using the quotient rule.

P'(t) = (0(1 + 7e^(-0.02t))- 1600(7 * -0.02e^(-0.02t)))/(1 + 7e^(-0.02t))^2

P'(t) = (224e^(-0.02t))/(1 + 7e^(-0.02t))^2

b) Just evaluate the derivative at t= 5.

P'(5) = (224e^(-0.02* 5))/(1 + 7e^(-0.02(5)))^2~~202.55 cells"/"day"

Hopefully this helps!