champ0007 wrote:A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a population of 5 million to 40 million in one hour, by what factor does the population increase every 10 minutes?
I did not understand the answer explanation, I tried to use Geometric Progression, but that is not working for me
Thanks
Use the formula for exponential growth:
Final Amount = Original Amount * (Multiplier)^(Number of changes)
In the problem above:
Final Amount = 40,000,000
Original Amount = 5,000,000
Multiplier = x
Number of changes = 6 (We're looking for the change over 10 minutes, and this change will occur 6 times over the course of 60 minutes.)
Plugging these values into the formula:
40,000,000 = 5,000,000 * x^6
8 = x^6
x = 8^(1/6) = √2.
For many test-takers, the easiest approach would be to plug in the answer choices, which an actual GMAT question would include.
The answer choices would represent the factor by which the population increases every 10 minutes.
Over 60 minutes, the population would be multiplied by the given factor 60/10 = 6 times.
Answer choice: √2.
5,000,000 * (√2)^6 = 5,000,000 * 8 = 40,000,000.
The correct answer is [spoiler]√2[/spoiler].
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