The population of a colony of bacteria triples in 3 days. Assuming that the rate of growth is proportional to the size of the population, how long did it take for the colony to double in size?
A) 2 days
B) 1.9 days
C) 4.9 days
D) 6 days
E) none of these

Question

Quizplus · Accepted Answer

Let P be the population of the colony and t be the time it takes for the population to double. 
Then we can write: 
2P = P * e^(r*t), where r is the growth rate. 
Since the population triples in 3 days, we know: 
3P = P * e^(r*3), which simplifies to: 
e^(r*3) = 3. 
Taking the natural logarithm of both sides gives: 
r * 3 = ln(3), so r = ln(3)/3. 
Substituting this value of r into the first equation yields: 
2P = P * e^[(ln(3)/3)*t], which simplifies to: 
2 = e^[(ln(3)/3)*t]. 
Taking the natural logarithm of both sides gives: 
ln(2) = (ln(3)/3)*t, so t = (3/ln(3)) * ln(2) ≈ 1.9 days.

The Population of a Colony of Bacteria Triples in 3