Blog 2 Answer:
a.
An example of real world
application of rate of change can be examined by the change in temperature of a
city at different time in a day.
b.
How can I find the temperature of
city at exactly 8.00? This can be determined by reading the value of
temperature that corresponds to exactly 8:00 time.
c.
The table is:
|
TIME
|
TEMPERATURE(0C)
|
|
08:00
|
15
|
|
10:00
|
17
|
|
12:00
|
22
|
|
14:00
|
21
|
|
17:00
|
20
|
|
18:00
|
16
|
|
21:00
|
11
|
|
|
|
d.
The graph of the table will be:
e.
Calculating the slope at
three different points on the graph, Change in
temperature with respect to time will give the rate of change of temperature. In
the above graph the three secant line is can be obtain from these four points
Let points A (10, 17), B (12, 22) C
(14, 21) and D (18, 16)
For the line AB the slope will be:
M1 = (22 -
17)/ (12 - 10)
= 2.5
For line AC the slope will be
M2
= (21 - 17)/ (14 - 10)
= 1
For
line AD the slope will be
M3
= (16 - 17)/ (18 - 10)
= -0.125
f.
The ARC of these lines represents
the same thing that was observed and recorded during the experiment. Therefore
the graph with the secant line will be like below:
The red line in the graph represents the line which passes through
point A. It will be the line by which we can calculate the rate of change of
temperature with respect to time. It can be accomplish by the secant line drawn
in the above graph by taking another point Q on the secant line. Find the slope
of line joining point A and Q. the point A is one through which all the secant
line has passed. This slope will give the rate of change of temperature with
respect to the time.
g.
We can see there are different rate
of change of speed for the intervals. In the entire interval the rate of change
of temperature is constant throughout the interval. The calculation of rate of
change of speed with respect to time is known as temperature gradient. Its unit
is oC/hour.
h.
In our experiment I have study the
change in temperature of a city in a day at different time. I have identified
the relation and variation of temperature as time goes from morning to evening.
And find the time interval in which it increases and decreases. I have also
come to know that how ARC is estimated in the graph and determination of rate
of change with respect to time.
your explanation is clear and you showed the changes in the temperatures from day to night very explicitly
ReplyDeleteYour blog is well structured and organized. Answers and explanations are very clear and well explained.
ReplyDeleteI like your scenario you chose-- time vs temperature. I found it fascinating to see how much temperature changes as time goes on. Your explanation is clear.
ReplyDeleteYour explanation is well written and clearly done! well done
ReplyDeleteGreat work. You're explanations show you put a lot of work into this.
ReplyDeleteAwesome job with the graphs! Your organization and presentation show you spent a lot of time on the assignment!
ReplyDeletereem,
ReplyDeleteyour application is good and i enjoyed reading it! your graphs and tables are clear and easy to read.
in the beginning, you state that you are going to find the change in temperature at exactly 8am, but then in your calculations, you show arc calculations for t = 10am. so, just try to be consistent, and also remember to include units in your secant calculations. the other thing that would have been good to see is the values that you used to do the tangent line calculation.
other than those few missing elements, you did a good job. =]
professor little