a. Charitable Contributions by Income
b. Using data
from tax filings, I found a table showing charitable contributions that were
deducted from taxes as a percentage of the individual’s income. So for those who donated to charities and
deducted it from their taxes, we are able to see the average amount donated as
a percentage of that income level. This
experimental application could be used to determine the effects of a $1,000
increase in income on the average individual’s donation behavior.
e. Using the
slope function in Excel, I was able to calculate the slope of the secant lines.
The slope between the $67,500 and $375,000 values is
-0.0026, so for every $1,000 increase in income between these points, the
percentage of income donated declines by 0.0026%.
The slope between the $67,500 and $225,000 values is -0.0057,
so for every $1,000 increase in income between these points, the percentage of
income donated declines by 0.0057%.
The slope between the $67,500 and $150,000 values is -0.0085,
so for every $1,000 increase in income between these points, the percentage of
income donated declines by 0.0085%.
The difference in these slopes shows that the line is steep
at first, but starts to level off as the income reaches $375,000.
g. The IRC at
$67,500 is -.01524. This means that at
this specific point, the percentage of income donated declines by 0.01524%. Notice how as the second point values in the
secant line decrease, the ARC also decreases, nearing the IRC.
h. This is
the IRC because as the secant nears point P ($67,500), the average rate of
change is more representative of the instantaneous rate of change. We are simply zooming in on the point and
calculating a more specific rate of change.
Stuart,
ReplyDeleteYou picked a good topic when it came to your project. I thought it was interesting that you picked the of percentage charitable contributions. It makes your project unique compared to the other ones I have seen. It also looks like you know your way around excel! Good for you! Clear, nice numbers.
Hi Stuart,
ReplyDeleteI also thought your topic choice was quite interesting. Before looking at your graph, I thought it would be the other way around. Your work is clear and to the point. If I were to improve one thing, I would explain a little more of where you took the number for the calculations. Besides that, nice job!
Sveta
I found your calculations to be correct and thought your explanations for what the answers mean was helpful. I also enjoyed your explanation for the IRC. The zooming in example was a good explanation for what the IRC is.
ReplyDeleteHi Stuart,
ReplyDeleteI thought you picked a interesting topic and I enjoyed reading it. I though the calculations were correct and the explanations really helped me to read the graph and help understanding.
hi, stuart,
ReplyDeletei really like your example and especially as this topic is of great interest to me. your narrative about your experiment was well put and your graphical explanations are outstanding and detailed! i love how you showed both the secant lines and tangent line calculations on the graph to enhance the understanding of what is happening at that point.
as sarah said, the only thing i would have added was to actually show the values that you used to calculate the IRC but other than that, awesome job!
professor little