Posted by **Bob** on Tuesday, February 17, 2009 at 8:56pm.

francois is stokcing a new fish pond on his farm. The pond is filling slowly and the volume of water in it can support a certain number of fish,(variable-F). F=42m+250, where m is the number of months the pond has been filling.

the pond was stocked initially with 110 fish, a population that will grow at a rate of 8 percent per month. P=110(1.08) to the power of m. this is the equation that models the population of fish after m number of months.

when will p equal f?

what will happen after this point has been reached? explain your answer.

- Math -
**drwls**, Tuesday, February 17, 2009 at 10:07pm
P = F when

42 m + 250 = 110*1.08^m

That equation can be solved by iteration. If m = 30,

42 m + 250 = 1510

110*1.08^m = 1106

If m = 35

F = 42 m + 250 = 1720

P = 110*1.08^m = 1626

If m = 36

42 m + 250 = 1762

110*1.08^m = 1756

m is slightly more than 36 months

At longer times, P will exceed F, and fish will start to die because the pond is too small to support the population.

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