A bacteria population grows at a rate proportional to its size. The initial count was 400 and 1600 after 1 hour. In how many minutes does the population double?
A)20
B)25
C)30
D)35
E)40
F)45
G)50
H)55

Question

Quizplus · Accepted Answer

Let P(t) be the population after time t in minutes.

P(t) = 400e^kt   ------(1) (since the population is proportional to its size)

When t = 60, P(60) = 1600

1600 = 400e^(60k)

e^(60k) = 4

Taking logarithm both sides,

60k = ln(4)

k = ln(4)/60

Now we need to find t such that the population doubles i.e. P(t) = 800.

800 = 400e^(kt)

2 = e^(kt)

Taking logarithm both sides,

ln(2) = kt

t = ln(2)/k = ln(2)/(ln(4)/60) = 30 minutes (approx.)

Therefore, the answer is choice C, 30.

A Bacteria Population Grows at a Rate Proportional to Its