Population as a Function of Age The function

$P\left(a\right)=0.015a^2-4.962a+290.580$

represents the population P (in millions) of Americans that are a years of age or older.

(a) Identify the dependent and independent variables.

(b) Evaluate $P\left(20\right)$. Provide a verbal explanation of the meaning of $P\left(20\right)$.

(c) Evaluate $P\left(0\right)$. Provide a verbal explanation of the meaning of $P\left(0\right)$.

The function $P\left(a\right)=0.015a^2-4.962a+290.580$represents the population P (in millions) of Americans that are a years of age or older.

(a) Identify the dependent and independent variables.

(b) Evaluate $P\left(20\right)$. Provide a verbal explanation of the meaning of $P\left(20\right)$.

(c) Evaluate $P\left(0\right)$. Provide a verbal explanation of the meaning of $P\left(0\right)$.

The given function is $P\left(a\right)=0.015a^2-4.962a+290.580$.

As we know, the dependent variable is characterized as the variable whose quality depends on the estimation of another variable in its condition.

In this given function width="14" height="19" role="math">Pdepends on the estimation of another variable in its condition.

So the dependent variable is$P$.

In this given function variable $\mathit{a}$are independent of changes.

So the independent variable is$a$.

$$\begin{gathered} P\left(20\right)=0.015{\left(20\right)}^2-4.962\times 20+290.580 \\ P\left(20\right)=0.015\times 400-4.962\times 20+290.580 \\ P\left(20\right)=6-99.24+290.580 \\ P\left(20\right)=197.34 \end{gathered}$$

The meaning of $P\left(20\right)$is " There are $197.34$million Americans $20$years of age or older."

$$\begin{gathered} P\left(0\right)=0.015{\left(0\right)}^2-4.962\times 0+290.580 \\ P\left(0\right)=0-0+290.580 \\ P\left(0\right)=290.580 \end{gathered}$$

The meaning of $P\left(0\right)$is " There are $290.580$million Americans $0$years of age or older."