The tutor discusses the exponential growth constant with an example.

Let’s imagine a population, initially 100, doubles every 25 hours. To a biologist growing a culture, it’s probably an easy situation to consider.

Such a growth pattern would likely be modeled as follows:

P=100e^(kt)

where P is the population at any time t.

To find k, we use the fact that in 25 hours, the population will have doubled to 200:

200=100e^(25k)

Dividing both sides by 100, we arrive at

2=e^(25k)

Taking the natural log of both sides, we find

ln2=25k

Dividing both sides by 25, we come to

ln2/25=k

Therefore, the growth equation for this case is

P=100e^(tln2/25)

Generally, k, the growth constant, will be

ln2/(doubling time).

HTH:)

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, part one. Toronto:
  D.C. Heath and Company, 1989.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.