Question

The number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 3.5% per hour.

How many hours does it take for the size of the sample to double?


Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

Generic exponential growth model: y = Ao[1+r]^t

In this case: r = 3.5% = 0.035

y = 2Ao .....[the double of the initial value]

Then: 2Ao =Ao (1 + 0.035)^t

(1.035)^t =2

Take logarithm to both sides

t ln(1.035) = ln(2)

t = ln(2) / ln(1.035) = 0.693 / 0.0344 = 20.15

Answer: 20.15 hours.