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Calculus/Population Growth

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Expert: - 2/8/2011


Question
The rate of growth of a populations of fruit flies is proportional to the size of the population at any instant. If there were 180 flies after the second day of the experiment and 300 after the fourth day, how many flies were there in the original population?

Answer
The number is Ax^n, where A is the number at day 0 and n is the number of days.
We know that Ax^2 = 180 and Ax^4 = 300, so divide the two.
This gives x^2 = 300/180.  Now both number are divisible by 60, so x^2 = 5/3.

We can then take this value and put in into the 1st equation and get A(5/3) = 180.
Multiply both sides by 3/5 to get the value of A.  

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