The table shows the population of a city over the past five years. $$\begin{array} { c | c }
& \text { Population } \
\text { Year } & \text { (in millions of people) } \
\hline 0 & 65 \
1 & 65.5 \
2 & 67 \
3 & 69 \
4 & 71.5
\end{array}$$ We used this data to develop the quadratic function $f ( x ) = 0.373 x ^ { 2 } + 0.165 x + 65$ which models the population of the city y in millions in the year x. Use the model to find the estimated population in year 9.
A) 66,822,000
B) 65,538,000
C) 1,490,000
D) 1,490,000,000,000

Question

The table shows the population of a city over the past five years. $$\begin{array} { c | c } 
& \text { Population } \
\text { Year } & \text { (in millions of people) } \
\hline 0 & 65 \
1 & 65.5 \
2 & 67 \
3 & 69 \
4 & 71.5
\end{array}$$ We used this data to develop the quadratic function $f ( x ) = 0.373 x ^ { 2 } + 0.165 x + 65$ which models the population of the city y in millions in the year x. Use the model to find the estimated population in year 9.
A) 66,822,000
B) 65,538,000
C) 1,490,000
D) 1,490,000,000,000

Quizplus · Accepted Answer

Plugging $x = 9$ into the quadratic function $f(x) = 0.373x^2 + 0.165x + 65$, we get $f(9) = 0.373(9)^2 + 0.165(9) + 65 = 0.373(81) + 1.485 + 65 = 30.213 + 1.485 + 65 = 96.698$. Since the population is in millions, the estimated population in year 9 is 96.698 million, or 96,698,000 people, which is closest to option A.

The Table Shows the Population of a City Over the Past