Question

under certain laboratory conditions, an agar plate contrains B(t)= 100(2-e^-t) bacteria t hours after the start of the experiment.





a. how many bacteria are on the plate at the start of the experiment (t=0) ?




b. Show that the population is always increasing. (show B'(t) > 0 for all t > 0 )




c. What happens to the population B(t) after a "long" time?

Answer 1

For a, plug in the value \(t=0\) and solve for your function. \(B(0)=100(2-e^{0})\)

Answer 2

for b. take the derivative of the function.