A bacterial culture grows according to the function B(t)= 800 1+3e^ -0.4t

MATHEMATICS · Multi-part · AP · Calculus BC · Differential Equations · Differential Equations

Problem

A bacterial culture grows according to the function

B(t)=\frac{800}{1+3e^{-0.4t}},

where

B(t)

is the number of bacteria present

t

hours after the start of the experiment. (a) Calculate the instantaneous growth rate

\dfrac{dB}{dt}

t=0

. (b) Determine the exact time

t

at which the population first reaches

600

bacteria. Provide your answer to the nearest hundredth of an hour. (c) Compute the growth rate

\dfrac{dB}{dt}

at the time found in part (b) and interpret its sign and magnitude in the context of the culture.