A bacteria culture initially contains 1500 bacteria and doubles every half hour.
Find the size of the baterial population after 20 minutes.
Find the size of the baterial population after 9 hours.
Answer
Final Answer: The size of the bacterial population after 20 minutes is approximately \(\boxed{2381}\) and after 9 hours is \(\boxed{393216000}\).
Step 1 ：This problem involves exponential growth, which can be represented by the formula \(P = P0 * e^{rt}\), where \(P\) is the final amount, \(P0\) is the initial amount, \(r\) is the growth rate, and \(t\) is the time.
Step 2 ：In this case, the initial amount of bacteria (\(P0\)) is 1500, the growth rate (\(r\)) is 2 per half hour, and the time (\(t\)) is given in the question.
Step 3 ：However, since the growth rate is given per half hour, we need to convert the time from hours or minutes to half hours. For the first question, 20 minutes is 2/3 of a half hour. For the second question, 9 hours is 18 half hours.
Step 4 ：Substituting these values into the formula, we get \(P1 = 1500 * e^{2*0.6666666666666666} = 2381.101577952299\) and \(P2 = 1500 * e^{2*18} = 393216000\).
Step 5 ：Rounding these values to the nearest whole number, we get \(P1 = 2381\) and \(P2 = 393216000\).
Step 6 ：Final Answer: The size of the bacterial population after 20 minutes is approximately \(\boxed{2381}\) and after 9 hours is \(\boxed{393216000}\).
