MHB Jordan's Question from Facebook (About Exponential Functions)

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Jordan is seeking help with a problem related to exponential functions, specifically the second part of an assignment he missed in class. A response suggests starting with the standard form of the exponential function, \(y=Ae^{mx}\), and using given values to create two equations. By dividing these equations, Jordan can solve for the variable \(m\). This guidance aims to help him progress with the problem. Understanding the method for solving exponential functions is crucial for completing the assignment.
Sudharaka
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Jordan from Facebook writes:

Got the first one right, don't know exactly what it's asking for in the 2nd part(I missed the class that we went over these types of problems) thanks!

2rgdzfa.jpg
 
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Sudharaka said:
Jordan from Facebook writes:

Got the first one right, don't know exactly what it's asking for in the 2nd part(I missed the class that we went over these types of problems) thanks!

2rgdzfa.jpg

Hi Jordan, :)

Start with the standard form of the exponential function, \(y=Ae^{mx}\) and plug in values for \(x\) and \(y\). You get two equations,

\[y_0=Ae^{mx_0}\]

\[y_1=Ae^{mx^1}\]

By dividing the two equations you'll be able to find \(m\). I hope you can continue from here. :)

Kind Regards,
Sudharaka.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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