A bacterial culture in a laboratory dish has population (in cells) modeled by P(t)=…
MATHEMATICS · Multi-part · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A bacterial culture in a laboratory dish has population (in cells) modeled by
P(t)=1+9e−0.4t10000,t≥0,
where t is measured in hours.
(1) Calculate the average rate of growth of the culture on the interval 0≤t≤5. Include units.
(2) Determine the instantaneous growth rate at t=5 hours.
(3) Show analytically that the growth rate attains its maximum at the time when e−0.4t=91. Find this time to the nearest tenth of an hour.
(4) Interpret the biological meaning of the results from parts (a)–(c), particularly the time of maximum growth rate, in the context of the bacterial culture’s development.