Exp growth

[Jinglander]

can someone explain how to solve questions like these. I am looking both for a general strategy and a solution.

The answer is sqrt(2)

A strain of bacteria mulitplies such that the ratio of its population in any two consectuive minutes is constant. If it grow from a population of 5 mil to a pop of 40 mil in 1 hour, by what factor does the population increase in 10 minutes

[limestone]

If the pop is double after a period then pop is
2 folds after 1 period
2^2 folds after 2 periods
2^3 folds after 3 periods
.......
(original pop factor is 1)
The pop of bacteria increases 8 folds after 60 minutes ( 40/5 =8). Now if one period is 10 minutes we have 6 periods here.
The same rule as above:
x^6 = 8 = 2^3
x^2 = 2, then x = sqrt(2)

Another example, if I take 20 minutes as a period, I have 3 periods here, and
x^3 = 8, x = 2
if a period is 30 minutes, x^2 = 8, then x = 2 * sqrt(2)

Hope this can help.