Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of

8.3%
per hour. How many hours does it take for the size of the sample to double?
Note: This

Answer 1

For this case we have a function of the form:

`y = A * (b) ^ t`
Where,
A: it is the initial amount of bacteria
b: growth rate
t: it's time
By the time the bacteria are double we have that y = 2A
Substituting values:

`2A = A * (1,083) ^ t`
From here, we clear t:

`(1,083) ^ t = 2 log1.083 ((1.083) ^ t) = 2 t = log1.083 (2) t = 8.7 hours`
Answer:
it takes for the size of the sample to double about:

`t = 8.7 hours`