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Problem 12 Easy Difficulty

The number, $N$, of bacteria in a culture at time $t,$ in hours, is $N(t)=1000\left[30+e^{-\frac{1}{5}}\right]$
a. What is the initial number of bacteria in the culture?
b. Determine the rate of change in the number of bacteria at time $t$.
c. How fast is the number of bacteria changing when $t=20 ?$
d. Determine the largest number of bacteria in the culture during the interval $0 \leq t \leq 50$.
e. What is happening to the number of bacteria in the culture as time passes?

Answer

a. 31000
b. $-\frac{100}{3} e^{-\frac{1}{6}}$
c. -17 bacteria/h
d. 31000 at time $t=0$

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Video Transcript

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