Question

40 point question!! Functions. (ignore pencil marks)

Answer 1

`\textsf{D)} \quad P(n)=0.024n^2-0.3n+4.3`

Explanation:

From inspection of the graph, when the number of coils is 10, the length of the spring is between 0 cm and 20 cm.

Substitute n = 10 into the equation of each given answer option:

`\begin{aligned}\textsf{Option A}: \quad P(10)&=10^2+4.3\\ & =100+4.3\\&=104.3\end{aligned}`

`\begin{aligned}\textsf{Option B}: \quad P(10)&=10^2-0.3(10)+4.3\\ & = 100-3+4.3\\&=97+4.3\\&=101.3\end{aligned}`

`\begin{aligned}\textsf{Option C}: \quad P(10)&=0.24(10^2)+4.3\\&=0.24(100)+4.3\\&=24+4.3\\&=28.3\end{aligned}`

`\begin{aligned}\textsf{Option D}: \quad P(10)&=0.024(10^2)-0.3(10)+4.3\\ & = 0.024(100)-3+4.3\\&=2.4-3+4.3\\&=-0.6+4.3\\&=3.7\end{aligned}`

Therefore, as 0 < P(10) < 20, the only suitable equation is Option D:

`\boxed{P(n)=0.024n^2-0.3n+4.3}`