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

40 point question!! Functions. (ignore pencil marks)-example-1
User Hazel
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4 votes

Answer:


\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}

User Pradeep Kashyap
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