Solve the problem.
-The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its
Primary food source. If $$P ( x ) = 3 x ^ { 2 } + 2$$ and s(a) = 2a + 5, what is the relationship between the predator mammal
And the plant food source?
A) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 4 \mathrm { a } ^ { 2 } + 20 \mathrm { a } + 27$
B) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$
C) $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$
D) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } ^ { 2 } + 60 \mathrm { a } + 77$

Question

Solve the problem.
-The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its
Primary food source. If $$P ( x ) = 3 x ^ { 2 } + 2$$ and s(a) = 2a + 5, what is the relationship between the predator mammal
And the plant food source? 
A) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 4 \mathrm { a } ^ { 2 } + 20 \mathrm { a } + 27$
B) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$
C) $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$
D) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } ^ { 2 } + 60 \mathrm { a } + 77$

Quizplus · Accepted Answer

To find the relationship between the predator mammal and the plant food source, we substitute $s(a) = 2a + 5$ into $P(x)$, treating $s(a)$ as $x$. So, $P(s(a)) = 3(2a + 5)^2 + 2$. Expanding this gives $P(s(a)) = 3(4a^2 + 20a + 25) + 2 = 12a^2 + 60a + 75 + 2 = 12a^2 + 60a + 77$.

Solve the Problem P(x)=3x2+2P ( x ) = 3 x ^ { 2 } + 2P(x)=3x2+2

Solve the Problem $P ( x ) = 3 x ^ { 2 } + 2$