Suppose a certain population of bacteria will grow exponenti

Suppose a certain population of bacteria will grow exponentially with a growth constant k =1/4. Find the time it will take for the population to triple in size.

Solution

k = 1/4
P(t) = P₀e^kt = P₀e^t/4

P(t) = 3P₀ = P₀e^t/4

3 = e^t/4

t/4 = ln(3)

t = 4ln(3) = 4.394