For a particular salmon population, the relationship between the number S of spa

Question

For a particular salmon population, the relationship between the number S of spawners and the number $ of offspring that survive to maturity is given by the formula R=4500s/s+500). Under what conditions is R>S?

Explanation / Answer

so if we want to find the values that satisfy the inequality R>S , we first have to find the exact amount in which they are the same: so the condition is R = S, so plugging that in to the given equation yields: S = 4500S / (S + 500) = S^2 + 500S = 4500S = S ( S - 4000) = 0 so S can take the value 0 and 4000 where the amount spawn and the amount that remain is the same, so we have to check the out come if S is less than 0, more than 0, less than 4000, and more than 4000 and figure what than means in terms of R. so since S can never negative, we don't test that so what if S was 1, then S = 1 and R = 4500/501 which is more than 1, so that doesn't work since 1 is less than 4000 we don't need to test another value below 4000, so lets test a number above 4000. when S = 4001 then R = 4000.111 which is larger than S. so the condition is that S > 4000

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