Chapter 5.1, Problem 24E

Growth of Bacteria Approximately $10,000$ bacteria are placed in a culture. Let $P\left(t\right)$ be the number of bacteria present in the culture after $t$ hours, and suppose that $P\left(t\right)$ satisfies the differential equation.

$P\text{'}\left(t\right)=0.55P\left(t\right)$.

a. What is $P\left(0\right)$?

b. Find a formula for $P\left(t\right)$.

c. How many bacteria are there after $5$ hours?

d. What is the growth constant?

e. Use the differential equation to determine how fast the bacteria culture is growing when it reaches $100,000$.

f. What is the size of the bacteria culture when it is growing at a rate of $34,000$ bacteria per hour?