Calculus-Asymptote

Question

Under certain laboratory conditions, an agar plate contains B(t) = 400(3 − 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

B(t) = 1200-400e^-t

 

a. at t=0, B(0) = 1200-400 = 800 bacteria

 

b. B'(t) = 400e^-t.....this derivative will always be positive because an exponential function with a positive base & positive coefficient can never be negative. 

 

c. When t gets very large, the exponential function to go toward zero, and this would mean the entire function would be moving toward 1200.