There is a population of thousand bacteria in a culture at time t hours after the beginning of an experiment. You know that , , and . Using these values, make a prediction for
A)0.302
B)0.304
C)0.306
D)0.308

Question

There is a population of  thousand bacteria in a culture at time t hours after the beginning of an experiment. You know that  ,  , and  . Using these values, make a prediction for 
A)0.302 
B)0.304 
C)0.306 
D)0.308

Quizplus · Accepted Answer

We know that the population is increasing exponentially, so we need to use the formula:

N(t) = N0 * e^(rt)

where N0 is the initial population, r is the growth rate, and t is the time.

Using the given values, we have:

N0 = 11
N(4) = 27
N(8) = 81
N(12) = ?

To solve for r, we can use the fact that:

N(t2)/N(t1) = e^(r(t2-t1))

Using t1 = 4 and t2 = 8, we have:

N(8)/N(4) = e^(r(8-4))
81/27 = e^(4r)
3 = e^(4r)
ln(3) = 4r
r = ln(3)/4

Now we can use this value of r to find N(12):

N(12) = N0 * e^(r*12)
N(12) = 11 * e^(ln(3)/4 * 12)
N(12) = 11 * e^3
N(12) = 11 * 20.0855
N(12) = 220.9405

Therefore, the predicted population at 12 hours is 220.9405 thousand, which rounds to 0.304 million. So the answer is B.

There Is a Population of Thousand Bacteria in a Culture