Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.
\begin{tabular} { l | l l l l l l l l l l l l }
Month & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \
\hline Temperature $\left( { } ^ { \circ } \mathrm { F } \right)$ & 19 & 27 & 38 & 45 & 57 & 62 & 65 & 58 & 51 & 41 & 33 & 25
\end{tabular}
Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$. Use the sine regression feature to do this. Approximate all values to one decimal place.
A) $f ( x ) = 22.5 \sin ( 0.5 ( x + 1.6 ) ) + 40.7$
B) $f ( x ) = 25.7 \sin ( 0.5 ( x + 1.6 ) ) + 32.5$
C) $f ( x ) = 22.5 \sin ( 0.5 ( x + 3.2 ) ) + 40.7$
D) $f ( x ) = 22.5 \sin ( 1.25 ( x + 1.6 ) ) + 40.7$

Question

Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.
\begin{tabular} { l | l l l l l l l l l l l l } 
Month & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \
\hline Temperature $\left( { } ^ { \circ } \mathrm { F } \right)$ & 19 & 27 & 38 & 45 & 57 & 62 & 65 & 58 & 51 & 41 & 33 & 25
\end{tabular}
Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$. Use the sine regression feature to do this. Approximate all values to one decimal place.
A) $f ( x ) = 22.5 \sin ( 0.5 ( x + 1.6 ) ) + 40.7$
B) $f ( x ) = 25.7 \sin ( 0.5 ( x + 1.6 ) ) + 32.5$
C) $f ( x ) = 22.5 \sin ( 0.5 ( x + 3.2 ) ) + 40.7$
D) $f ( x ) = 22.5 \sin ( 1.25 ( x + 1.6 ) ) + 40.7$

Quizplus · Accepted Answer

The correct model for the data is $f(x) = 22.5 \sin(0.5(x + 1.6)) + 40.7$. This is because the amplitude (22.5) represents the variation from the average temperature (40.7), the frequency (0.5) adjusts for the period of the cycle over the year, and the phase shift (1.6) aligns the model with the data's starting point.

Solve the Problem (∘F)\left( { } ^ { \circ } \mathrm { F } \right)(∘F)

Solve the Problem $\left( { } ^ { \circ } \mathrm { F } \right)$