Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 6.2% per hour. How many hours does it take for the size of the sample to double?

Note: This is a continuous exponential growth model.

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

Pls pls pls pls please actually answer, like I have spent an HOUR ON ONLY THIS QUESTION.

Answer 1

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

In this case: r = 6.2% = 0.062

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

Then: 2Ao =Ao (1 + 0.062)^t

(1.062)^t =2

Take logarithm to both sides

t ln(1.062) = ln(2)

t = ln(2) / ln(1.062)

11.1789

Hence, the population doubles in 11.18 days

Answer 2

Refer to the attached image.

Answer:
`t \approx 11.18 \ days`