Question

A water tank is contaminated with a colony of 20 000 e.Coli bacteria. After 3 days the bacteria has grown to 28 284 e. Coli. What is the doubling time of the bacteria using an equation

Answer 1

6

Explanation:

The formula for doubling time is given as:

P(t) = Po(2)^t/k

Where:

P(t) = Population after time t = 28,284

Po = Initial Population = 20,000

t = time = 3 days

k = doubling time = ?

28,284 = 20,000 × (2)^3/k

Divide both sides by 20,000

28,284/20,000 = 20,000/20,000 × (2)^3/k

1.4142 = (2)^3/k

2^1/2 = (2)^3/k

Divide both sides by 2

1/2 = 3/k

Cross Multiply

k × 1 = 2 × 3

k = 6

Therefore, the doubling time(k) of the bacteria is 6