Question Suppose a bacterial culture triples in population every 5 hours. If the population is initially 200 , (a) quickly determine when the population will reach 5400 . (b) Find an equation for the population at any time. (c) Determine when the population will reach 20,000 .

Step 1 ：Use the exponential growth formula: \(P(t) = P_0 * (r^t)\), where \(P(t)\) is the population at time \(t\), \(P_0\) is the initial population, \(r\) is the growth rate, and \(t\) is the time.

Step 2 ：Calculate the growth rate: \(r = 3^{(1/5)} = 1.24573\)

Step 3 ：\(a)\) Find when the population reaches 5400: \(5400 = 200 * (1.24573^t)\), solving for \(t\), we get \(t \approx 15\) hours.

Step 4 ：\(b)\) The equation for the population at any time is: \(P(t) = 200 * (1.24573^t)\)

Step 5 ：\(c)\) Find when the population reaches 20000: \(20000 = 200 * (1.24573^t)\), solving for \(t\), we get \(t \approx 20.96\) hours.

Step 6 ：\(\boxed{\text{Final Answer:}}\) \(a)\) 15 hours, \(b)\) \(P(t) = 200 * (1.24573^t)\), \(c)\) 20.96 hours