## Related questions with answers

Suppose the population P of a certain species of fish depends on the number x (in hundreds) of a smaller kind of fish that serves as its food supply, where $P(x)=2 x^{2}+1$. Suppose, also, that the number x (in hundreds) of the smaller species of fish depends on the amount a (in appropriate units) of its food supply, a kind of plankton, where x=f(a)=3a+2. Find $(P \cdot f)(a)$, the relationship between the population P of the large fish and the amount a of plankton available.

Solution

Verified$\begin{align*} (p \circ f)(a)&=p\left(f(a)\right) && \\\\ &= p(3a+2)&& {\color{#c34632} \text{Substitute $3a+2$ for $f(a)$}} \\\\ &= 2(3a+2)^2 +1 && {\color{#c34632} \text{Substitute $3a+2$ for $x$ in the function $p(x)=2x^2+1$}} \\\\ &= 2(9a^2+12a+4) +1 && {\color{#c34632} \text{Use the formula $(a+b)^2=a^2+2ab+b^2$}} \\\\ &= 18a^2+24a+8 +1 && {\color{#c34632} \text{Multiply}} \\\\ &= 18a^2+24a+9 && {\color{#c34632} \text{Combine like terms}} \\\\ \end{align*}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Algebra and Trigonometry for College Readiness

1st Edition•ISBN: 9780131366268John Hornsby, Margaret L. Lial## More related questions

- anatomy and physiology

1/4

- anatomy and physiology

1/7