The population is increased in 30 hours by a factor of 64.
The population is increased in 1 week (168 hours) by a factor of \(1.302\times 10^{10}\).
The doubling time is time required to double the population, the population ratio between two consecutive times is defined by this expression:
\(r = 2\) (1)
By mathematical induction, we can predict the population ratio between non-consecutive times by using the following formula:
\(r = 2^{\frac{t}{T} }\) (2)
Where:
- \(t\) - Time, in hours.
- \(T\) - Period, in hours.
The population is increased in 30 hours at the following factor: (\(t = 30\,h\), \(T = 5\,h\))
\(r = 2^{\frac{30\,h}{5\,h} }\)
\(r = 2^{6}\)
\(r = 64\)
The population is increased in 30 hours by a factor of 64.
The population is increased in 1 week (168 hours) at the following factor: (\(t = 168\,h\), \(T = 5\,h\))
\(r = 2^{\frac{168\,h}{5\,h} }\)
\(r = 1.302\times 10^{10}\)
The population is increased in 1 week (168 hours) by a factor of \(1.302\times 10^{10}\).
We kindly invite to check this question on doubling times: https://brainly.com/question/3580579
