Question

A simplified model for the concentration (micrograms/milliliter) of a certain slow-reacting antibiotic in the bloodstream t hours after injection into muscle tissue is given by
f(t) = t2 ·e−t/16, t ≥ 0.
When will there be maximum concentration?
In the units given, how much is the maximum concentration?
When will the concentration dip below a level of 20.0?
Estimate from a graph when the concentration function changes concavity

Answer 1

Answer:

A) T = 24

b) 77.953

c)  t > 63.78 , t < 5.6

d) (7.029,27.5) and (40.97,55.23)

Step-by-step explanation:

Given

F(t) = t^2 e^-t/12, t ≥ 0

a) time for maximum concentration

  t = 24

b) determine maximum concentration at maximum time

F(24) = 77.953

c) determine when the concentration will dip below the level of 20.0

when t > 63.78 , t < 5.6

d) concentration function changes concavity  ( estimated from a graph )

(7.029,27.5) and (40.97,55.23)

attached below is the detailed solution