Blog #2

A. A real world application of rate of change would be to examine the average rate that the monthly temperature changes in D.C from January to August. (Month/Time) 

While results may vary, we will use the average temperatures gathered from 1981 – 2010 at the Ronald Reagan Washington National Airport in Arlington, Virginia.

B. As winter ends and it gets warmer, people always wonder how fast the weather will get warmer. Thus, we will figure out at what the average rate of change in temperature in February (b/c we are literally in February)

http://www.currentresults.com/Weather/US/washington-dc-temperatures-by-month-average.php

C.

This graph represents the average temperature of each month in Washington, DC.

Months	1	2	3	4	5	6	7	8
Temp (F)	36	39	47	57	66	75	79.5	78.5

This second graph takes January’s temperature and changes it to zero to accurately measure how fast the temperature actually goes up.

Months	1	2	3	4	5	6	7	8
Temp (Change)	0	3	11	21	30	39	43.5	42.5

D.

E. My three-secant lines will be from February (2) to March (3), February (2) to May (5), and February (2) to July (7).

So the ARC from February (2) to March (3) is (11-3)/(3-2) = 7

From February (2) to February (5) is (30 – 3)/(5-2) = 10

From February (2) to July (7) is (43.5 – 3)/(7-2) = 8.1

Mean/ARC = 8.37 Fahrenheit/Month

This basically shows that the slope of temperature increase in the Washington, DC area from January to August is approximately 8.37 degrees/Fahrenheit per month.

F. Tangent line that passes through point P=2

G. The second point in the graph is point Q on the tangent line and the slope of the line (PQ) is

Point P (2, 3) and Point Q (5.2, 24.3) where x values represents months and y values represent temperature increase

Slope (IRC): (24.3 – 3)/(5.2-2)= 6.65 degrees Fahrenheit/month

The IRC ended up being different than the ARC we calculated in part E. There are various factors that could have been the factor to these two numbers not being the same (estimations being made in drawing the line as well as Point Q). However, the two numbers are very close that allows us to believe our application is not completely wrong. Additionally, without a doubt, the temperature is increasing because of the positive rates of change. This means that during February, the temperature should be increasing approximately 6.65 degrees Fahrenheit/month.

H. I know that this is the IRC because the change in temperature becomes significant the later it gets in spring. You can’t really expect it to change that much in the beginning. The slope becomes much steeper after February and thus, it is becoming significantly warmer. Also as it says in the assignment, the values of the calculations from part d are getting smaller and thus the slope of the secant is getting closer to tangent line to provide a more accurate prediction of the temperature increase/change per month.