Question

A certain number of bacteria are in a petri dish. If the growth rate is 2.7 percent per hour, how many hours will it take the bacteria to double in number?
A) 25.95 hours
B) 20.29 hours
C) 2.595 hours
D) 2.029 hours

Answer 1

Answer: option A) 25.95 hours

Explanation:

1) growth rate = 2.7% ⇒ r = 1 + 2.7/100 = 1.027

2) growth equation:

Calling N the number of bacteria at any time, No the initial number of bacteria, and n the number of hours elapsed, you can write this growing equation:


N = No × (1.027)ⁿ

3) double in number

That means that N = 2 No, so replacing in the equation you get:

2No = No = (1.027)ⁿ

Dividing both sides by No, you get:

2 = (1.027)ⁿ

4)  To solve use logarithm properties

log (2) = n log (1.027)

⇒ n = log (2) / log (1.027) = 0.301 / 0.0116 = 25.95