## Related questions with answers

Suppose the population $P$ of a certain species of fish depends on the number $x$ (in hundreds) of a smaller fish that serves as its food supply, so that

$P(x)=2 x^{2}+1.$

Suppose, also, that the number of the smaller species of fish depends on the amount a (in appropriate units) of its food supply, a kind of plankton. Specifically, $x=f(a)=3 a+2$. A biologist wants to find the relationship between the population $P$ of the large fish and the amount a of plankton available, that is,$P[f(a)]$. What is the relationship?

Solution

VerifiedWe suppose that the population $P$ of a certain species of fish depends on the number(in hundreds) of a smaller fish that serves as its food supply, so that

$\begin{aligned} P(x) = 2x^{2} + 1 \end{aligned}$

the number of the smaller species of fish depends on the amount a (in appropriate units) of its food supply, a kind of plankton. Specifically,

$x= f(a) = 3a + 2.$

where $a$ is the amount (in approximate units) of food supply on which the smaller species of fish depends.

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