Chapter 6.6, Problem 20E

To determine

To find the number of daylight hours for middle of each month or average monthly temperature and also write a sinusoidal function to model data.

Answer to Problem 20E

  $y=1.61\sin \left(\frac{\pi }{6}t-c\right)+12.14$

Explanation of Solution

The data can be modeled by the function of the form $y=A\sin (kt-c)+h$ , where is the time in months. First find $A,h$ and $k$

  $\begin{array}{l}A=\frac{13.75-10.53}{2}=1.61\\ h=\frac{13.75+10.53}{2}=12.14\\ k:\frac{2\pi }{k}=12\\ k=\frac{\pi }{6}\end{array}$

Substituting the above values in the equation to form the sinusoidal function as follows-

  $y=1.61\sin \left(\frac{\pi }{6}t-c\right)+12.14$

Therefore the model equation for number of daylight hours for middle of each month or average monthly temperature is number of daylight hours for middle of each month or average monthly temperature