Question

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) = 4x² + 7 and s(a) = 4a + 2, what is the relationship between the predator mammal and the plant food source?

O P(s(a)) = 16a² + 16a + 11
O P(s(a)) = 64a² + 32a + 23
O P(s(a)) = 64a² + 64a + 23
O P(s(a)) = 16a + 9

Answer 1

The relationship between the predator mammal and the plant food source can be determined by substituting the smaller animal population equation into the predator mammal population equation.

Step-by-step explanation:

The relationship between the predator mammal and the plant food source can be determined by the composition of the population equations. Given that P(x) = 4x² + 7 represents the population of the predator mammal depending on the number x of the smaller animal, and s(a) = 4a + 2 represents the population of the smaller animal depending on the amount a of the plant, we can substitute s(a) into P(x) to find the relationship.

Substituting s(a) into P(x):

P(s(a)) = 4(4a + 2)² + 7

Simplifying the expression:

P(s(a)) = 16a² + 16a + 11

Therefore, the relationship between the predator mammal and the plant food source is P(s(a)) = 16a² + 16a + 11.