Question 13 (3 points)
The population of a bacteria colony triples every hour. If the initial population is 100
a) write an equation that would model the population, where $P$ is the total population and $t$ is time in hours.
b) What is the population of the colony in 5 hours?

Step 1 ：The population of the bacteria colony triples every hour. This is an exponential growth situation. The general form of an exponential growth equation is \(P = P_0 * r^t\), where \(P\) is the final population, \(P_0\) is the initial population, \(r\) is the growth rate, and \(t\) is time. In this case, the initial population \(P_0\) is 100, the growth rate \(r\) is 3 (since the population triples), and \(t\) is the time in hours.

Step 2 ：To find the population of the colony in 5 hours, we can substitute \(t = 5\) into the equation.

Step 3 ：\(P_0 = 100\)

Step 4 ：\(r = 3\)

Step 5 ：\(t = 5\)

Step 6 ：\(P = 24300\)

Step 7 ：Final Answer: The population of the colony in 5 hours is \(\boxed{24300}\).