A ager plate contains B(t) = 600(4-e^-t) bacteria t hours after the start of the experiment. Show that the population is always increasing. (Show B’(t) >0 for all t > 0)

Answer 1

We have B(t) = 600 x (-4 x e^-t) Then

B^'(t) = 600 x 4 d(e^-t)/ dt Recall the derivative of the natural log is the natural log itself & using the chain rule we have:

B^'(t) = -600 x -4 x e^-t = 2400 x e^-t and since e^-t > 0 for t > 0

We have to prove the result.

Answer 2

B(t) = 600(4-e^-t) = 2400 - 600e^-t

B'(t) = -600(-e^-t) = 600e^-t

B'(t) is positive for all t, so B(t) is increasing for all t > 0