a. Recorded
data from a population growth of flies over a period of time of a day.
b. In
this problem, the population of flies becomes the dependent variable while time
becomes the independent variable. This is because the population of flies
depends on time. Question: what is the rate of change at 1300 hours?
c.
|
|
population
|
|
1200
|
23562300
|
|
1300
|
23546000
|
|
1400
|
30235600
|
|
1500
|
45621300
|
|
1600
|
23032012
|
|
1700
|
20132530
|
|
1800
|
25631250
|
d.
e. In
the above graph the three secants can be obtained from these three points.
Let
points A (1230, 240000000), B (1340, 30000000), C (1630, 20000000)
For line AB the slope will be:
M1= (30000000-24000000)/ (1340-1230)
=
5142857.143
For line AC slope will be
M2= (20000000-30000000)/(1630-1340)
=
35294111.765
The ARC of the secant lines increases and then
decreases a bit with the second calculation. With time rate of change on times
1230 and 1340 producing the highest number of population of flies, a population
of about 5 million flies. The calculations here represent the rate of change of
the population over a period of years.
f.
g. Calculation
of slope of the line
Change in population/ change in time
(45000000-23000000)/(1430-1300)
14,666,666.67
The calculation here does not represent the same
results that were calculated in the experiment. Though the calculation are very
reasonable according to the trend of the population of flies,
h. The
value from the part g above in the IRC due to the following reasons. From the
calculations that were seen earlier, all the answers were almost same to the
answer done before. This is evidence that a secant is getting closer and closer
to the tangent. We can therefore conclude that the population is increasing
with a constant number of flies.
Really interesting application. I was slightly confused by your x values. Can you explain further what those are? Overall it looks really good.
ReplyDeleteHello Mishal;
ReplyDeleteThis really funny application, finding the flies population growth. I do believe such report can benefit parties who are interested in controlling harmful insect population. Thanks.
It is really good. I like the fact how you used the graphics. Thanks for your hard work
ReplyDeletemishal,
ReplyDeletethis is a very curious topic. but it was interesting to read.
in the beginning, you state that you will find the change in population at t = 1300, but your calculations are surrounding the point t = 1340. please be consistent. additionally, the instructions asked for three secant lines calculations and you only showed two. also, in your next post, remember to include the units as they are not included with your secant line calculations.
let me know if you have questions.
professor little