Answer
a) $6796.55$
b) $4024.55$
c) See graph
d) In $1957$ with a value of $\$1406$
e) In 1939 and 1975
f) $[38997, 45972]$
Work Step by Step
Given $$\begin{aligned}
N(t) &= 155(t-9)^2 +33417.
\end{aligned}$$ a) Determine $N(t)$ for $t=2$: $$\begin{aligned}
N(2) &= 155(2-9)^2 +33417\\
&= 41012.
\end{aligned}$$. The number of people under the poverty level in $2002$ was about $41$ million people.
b) Determine $N(t)$ for $t=15$: $$\begin{aligned}
N(15) &= 155(15-9)^2 +33417\\
& = 38997.
\end{aligned}$$ This means that the number of people below the poverty level in $2015$ was about $39$ million people.
c) See the graph below.
d) The graph shows that the vertex is located at $(9,33417)$. This means that the number of people under the poverty level in $2009$ was about $33417$ thousand people which was the minimum record.
e) The graph shows that the number of people under the poverty level was about $37$ million in $2004$ and $2014$.
f) We can compute the range of the function from the values of the domain of the function. $$\begin{aligned}
N(3) &= 155(3-9)^2 +33417\\
&= 38997\\
N(18) &= 155(18-9)^2 +33417\\
&= 45972.
\end{aligned}$$ The range of the function is $[38997, 45972]$.
