Applied Calculus Project

[Phantasmagorickal]

Applied Calculus Problem

Hello everyone.

My name is Zara, I'm new to the forum and this is my first post! I'm in the process of coming up with an applied calculus project as a final project for my calculus I course.

Here are the requirements for the project:

1. Submit one real-world application and their complete solution that requires concepts in Calculus I in order to solve.
2. The real-world application and solution must be original (your own work) and/or cited if other work was adapted. You may not simply copy or modify an existing application and/or solution. Note: Word problems found in textbooks or websites, etc... are not an acceptable applied project.
3. Use APA style to cite any references (websites, books, journals, etc...) that are used to inspire your problems (and/or solutions).
4. The real-world application should be related to current events and should clearly demonstrate concepts in covered in our Calculus I (see Focus on Calculus example).
5. Your grade for this project will be based on (a) originality, (b) accuracy of problem and its solution, (c) relevancy to current events, and (d) relevance and clear connection to concepts addressed in our Calculus I course.

And here is my idea so far (please don't laugh) :

In 2013, approximately 13% of the energy sources used in the United States were renewable. According to a report released by GreenPeace U.S.A., it is economically feasible that nearly 80% of U.S. electricity can be produced by renewable energy sources by the year 2050.

a.) If the use of renewable energy was increased by a steady 2% annually from the year 2014, would the consumption of renewable energy reach 80% by the year 2050?

b.) If so, at what year would renewable energy consumption reach 80%?

I need some help on how to devise a formula in order to solve this problem I have created. Also if you have any suggestions on how my questions could be better, I'm open to that as well. I'm not great at this stuff so if anyone could help me find a place to start that'd be awesome.

Thanks for any help.

Sincerely,

Zara

 

[stapel]

Here are the requirements for the project:

1. Submit one real-world application and their complete solution that requires concepts in Calculus I in order to solve.
2. The real-world application and solution must be original (your own work) and/or cited if other work was adapted. You may not simply copy or modify an existing application and/or solution. Note: Word problems found in textbooks or websites, etc... are not an acceptable applied project.
3. Use APA style to cite any references (websites, books, journals, etc...) that are used to inspire your problems (and/or solutions).
4. The real-world application should be related to current events and should clearly demonstrate concepts in covered in our Calculus I (see Focus on Calculus example).
5. Your grade for this project will be based on (a) originality, (b) accuracy of problem and its solution, (c) relevancy to current events, and (d) relevance and clear connection to concepts addressed in our Calculus I course.

And here is my idea so far (please don't laugh) :

In 2013, approximately 13% of the energy sources used in the United States were renewable. According to a report released by GreenPeace U.S.A., it is economically feasible that nearly 80% of U.S. electricity can be produced by renewable energy sources by the year 2050.

a.) If the use of renewable energy was increased by a steady 2% annually from the year 2014, would the consumption of renewable energy reach 80% by the year 2050?

You're supposed to use "concepts in Calculus I to solve" the puzzle you present. But question (a) above requires only algebra, being knowledge of the exponential-growth formula. Where will calculus come into play?

Please be specific. Thank you!

 

[Dale10101]

Seeking Calculus

Hello everyone.

My name is Zara, I'm new to the forum and this is my first post! I'm in the process of coming up with an applied calculus project as a final project for my calculus I course.

Here are the requirements for the project:



And here is my idea so far (please don't laugh) :

In 2013, approximately 13% of the energy sources used in the United States were renewable. According to a report released by GreenPeace U.S.A., it is economically feasible that nearly 80% of U.S. electricity can be produced by renewable energy sources by the year 2050.

a.) If the use of renewable energy was increased by a steady 2% annually from the year 2014, would the consumption of renewable energy reach 80% by the year 2050?

b.) If so, at what year would renewable energy consumption reach 80%?

I need some help on how to devise a formula in order to solve this problem I have created. Also if you have any suggestions on how my questions could be better, I'm open to that as well. I'm not great at this stuff so if anyone could help me find a place to start that'd be awesome.

Thanks for any help.

Sincerely,

Zara

In seeking a project one approach might be to consider the basic idea of finding the area under the curve.

Basic notion: area = length x height = (x)(y). Fine for squares and rectangles but suppose the height varies with length ... calculus is needed. area = Integrate[y(x), x] over some interval of x. Which you of course know. The point is to notice is that integration is fancy multiplication, that is, the units of the result are the product of x and y(x), say, square feet in this case.

In general then one type of calculus project would center around finding some quantity whose units are the product of the units of a function and those of its independent variable, rate x time for example, or a definition based on a product like, work = force x distance

Your project might fly if your rate of increase (2%) varied with time. Are there time dependent factors that will determine how quickly renewable resources are introduced ... projected increases of fossil fuel, projected decreases in solar panel cost, population growth?

Since the figures you cite are projected over time, somebody must be doing calculus somewhere. I would guess that part of the value of this project to to realize that. Good luck.