Chapter 1.4, Problem 14E

(a)

To determine

The model for the city of Syracuse with the use of graphing utility.

t	1	2	3	4	5	6	7	8	9	10	11	12
M	76.5	77.7	80.7	83.8	87.8	89.5	90.9	90.6	89.0	85.4	81.2	77.5
S	31.4	33.5	43.1	55.7	68.5	77.0	81.7	79.6	71.4	59.8	47.4	36.3

Where t denotes the month $M$ and $S$ denotes the temperature of the city of Miami and Syracuse in degree Fahrenheit.

(b)

To determine

To graph: The scattered plot for the data provided for the city of Miamialso plot the model function $M\left(t\right)=83.70+7.46\sin \left(0.4912t-1.95\right)$ provided for the city of Miami.

(c)

To determine

To graph: The scattered plot for the data provided for the city of Syracuse also plot the model function $S\left(t\right)=56.37+25.47\sin \left(0.5080t-2.07\right)$ provided for the city of Syracuse.

(d)

To determine

To calculate: The average annual temperature of each city (Miami and Syracuse).

(e)

To determine

To calculate: The period of the each model $S\left(t\right)=56.37+25.47\sin \left(0.5080t-2.07\right)$ and $M\left(t\right)=83.70+7.46\sin \left(0.4912t-1.95\right)$ as obtained in above part.

(f)

To determine

Which city has greater variability in temperature. Also determine the fact on which variability of temperature depends.