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?
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
#P'(5) = (224e^(-0.02* 5))/(1 + 7e^(-0.02(5)))^2~~202.55 cells"/"day"#
Hopefully this helps!
