I need help in doing my project in Calculus I. It is to be a Real-World Applicat

Question

I need help in doing my project in Calculus I. It is to be a Real-World Application in Calculus I (related to Science, Technology, Engineering, and/or Mathematics) and requires,

1. one real-world application and the complete solution that each requires concepts in Calculus I in order to solve.

2. The real-world application and its 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: Textbook word problems are NOT an acceptable applied project.

3.. These real-world applications should be related to current events and should clearly demonstrate concepts in covered in our Calculus I.

Any help is appreciated. I would like to see an equation for what an applicable Calculus problem is.

Explanation / Answer

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.

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