Nutrients in low concentrations inhibit growth of an organism, but high concentr

Question

Nutrients in low concentrations inhibit growth of an organism, but high concentrations are often toxic. Let d be the concentration of a particular nutrient (in moles/liter) and P| be the population density of an organism (in number/cm^2!). Suppose that it is found that the effect of this nutrient causes the population to grow according to the equation: P(c) = 200c/1 + 2500c^2. Find the concentration of the nutrient that yields the largest population density of this organism and what the population density of this organism is at this optimal concentration.

Explanation / Answer

you have to differentiate P wrt c and put dP/dc=0.

differentiate. we will get.

[(1+2500c^2)200-200c(5000c)]/(1+2500c^2)^2=0

c=1/50 moles/liter

P(1/50)=2/cm^2

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