The population P of a bacteria culture is modeled by , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.
A)54.8 hours
B)8.9 hours
C)79.9 hours
D)81.7 hours
E)56.6 hours

Question

The population P of a bacteria culture is modeled by  , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.
A)54.8 hours 
B)8.9 hours 
C)79.9 hours 
D)81.7 hours 
E)56.6 hours

Quizplus · Accepted Answer

To find out how long it takes for the population to double, we need to find the value of t in the equation when P = 2P_0 (where P_0 is the initial population).

2P_0 = 11eacce6_1fcf_fc98_9f49_172d8e953f64_TB7896_11

Dividing both sides by P_0:
2 = 11eacce6_1fcf_fc98_9f49_172d8e953f64_TB7896_11 / P_0

Taking the natural logarithm of both sides:
ln(2) = ln(11eacce6_1fcf_fc98_9f49_172d8e953f64_TB7896_11 / P_0)

Using the properties of logarithms:
ln(2) = ln(11eacce6_1fcf_fc98_9f49_172d8e953f64_TB7896_11) - ln(P_0)

Solving for t (time):
t = (ln(2) + ln(P_0)) / ln(11eacce6_1fcf_fc98_9f49_172d8e953f64_TB7896_11)

Plugging in P_0 = 5800 and rounding to the nearest tenth gives us:
t ≈ 79.9 hours

Therefore, the answer is choice C.

The Population P of a Bacteria Culture Is Modeled by