Question

A food sample contains 300 bacteria. The doubling time for bacteria left at room temperature is 20 minutes. How many minutes will it take to reach an unsafe level of 100000 bacteria?

Answer 1

167.6 minutes

Explanation:

The formula is given as:

P(t) = Po × (2)^t/k

Where

P(t) = Population after time t = 100000

Po = Initial population = 300

k = Doubling time = 20 minutes

t = Time = ?

Hence:

100000 = 300 × (2)^t/20

Divide both sides by 300

100000/300 = (300 × (2)^t/20)/300

333.3 = 2^t/20

Take the In of both sides

In 333.3 = In (2^t/20)

In 333.3 = t/20 In 2

Divide both sides by In 2

In 333.3/In 2 =( t/20 In 2)/In 2

8.3806775072 = t/20

Cross Multiply

t = 8.3806775072 × 20

t = 167.61355014 minutes

Approximately = 167.6 minutes

Therefore, the time it will take to reach an unsafe level of 100000 bacteria is 167.6 minutes