The population of a certain bacterial culture satisfies
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
The population P(t) of a certain bacterial culture satisfies dtdP=kP. The population triples in 11 minutes.
(a) Determine the exact value of the constant k.
(b) Write the explicit formula for P(t) assuming an initial population of P0 at time t=0.
(c) A health inspector requires the culture to remain below 40000 cells. If the initial population is 5500 cells, find the maximum length of time (in minutes, rounded to two decimal places) that the culture may be allowed to grow before reaching the inspector’s limit.