Question

the doubling time of a population of flies is 5 hours. by what factor does the population increase in 30 hours? By 1 week?

Answer 1

2/5 = x/30

5x = 60

60 ÷ 5 = 12

In 30 hours it would be 12 times the population.

12/30 = x/168

30x = 12 × 168 = 2016

2016 ÷ 30 = 67.2

By one week the population would increase by 67.2 times.

Answer 2

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 $1.302\times 10^{10}$.

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