Time and Temperature, Part 10

Home Assessment

Part A: Kalamazoo, MI

The following table shows long-term average temperatures in Kalamazoo, Michigan. (Source: Core-Plus Mathematics Project.)

**Average Temperatures**
**Kalamazoo, MI**
Month	Temperature (^oF)
Jan.	24
Feb.	27
Mar.	36
Apr.	49
May	60
June	69
July	73
Aug.	72
Sep.	65
Oct.	54
Nov.	40
Dec.	29

1. Enter the data in your graphing calculator and make a scatter plot.
2. Estimate the coefficients A, B, C, and D of a function of the form

f(x) = A sin [ B (x - C)] + D that should fit this data. Plot your sinusoidal function on the data. How good is the fit? 3. Adjust the coefficients as necessary to make the fit as good as you can.

Part B: Helsinki, Finland

Finland has a delightful web site to inform travelers about the Finnish weather. It includes normal ranges of temperatures for Helsinki for each month of the year. If we average the normal highs and lows for each month, we can derive the following table of data. Find the best fitting sine function for the Helsinki data.

**Average Temperatures**
**Helsinki, Finland**
Month	Temperature (^oC)
Jan.	-6.0
Feb.	-6.0
Mar.	-3.5
Apr.	4.0
May	7.0
June	14.0
July	16.5
Aug.	15.0
Sep.	10.5
Oct.	6.0
Nov.	0.5
Dec.	-2.5

Part C: Your choice

Every Chamber of Commerce in the country seems to have a web site that includes data on coldest and warmest months. The following table is a sampling of such data.

1. Choose one location, and construct a graph of the sinusoidal function that should approximate long-term average temperature at that location.

2. Use your graph to estimate average temperatures for one Spring month and one Fall month.

Location	Coldest month	Avg. Temp. (^oF)	Warmest month	Avg. Temp. (^oF)
Charlotte, NC	Dec.	39.3	July	79.3
Nappanee, IN	Jan.	23.4	July	72.5
Oakland, CA	Jan.	48.1	July	63.2
South Holland, IL	Jan.	12.2	July	83.8
Temple, TX	Jan.	36.0	July	96.0