Can You Create a Function that Triples Every 7 Starting at 20?

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SUMMARY

The discussion focuses on creating a mathematical function that starts at 20 and triples every 7 units. The solution involves utilizing exponential functions, specifically fitting the function to the conditions f(0)=20 and f(7x)=2f(x). By taking the derivative of the second condition and substituting it back into the original, a first-order differential equation is derived, leading to the exponential function as the solution. This method effectively combines calculus and exponential growth concepts to achieve the desired function.

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  • Understanding of exponential functions
  • Knowledge of differential equations
  • Familiarity with function notation and manipulation
  • Basic calculus skills
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  • Study the properties of exponential functions in depth
  • Learn how to solve first-order differential equations
  • Explore function fitting techniques in mathematics
  • Review calculus concepts related to derivatives and their applications
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Mathematicians, students studying calculus, and anyone interested in applying exponential functions to real-world problems will benefit from this discussion.

jared89
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write a function that starts at 20 and triples every 7
 
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I'm sure you have just learned about exponential functions!

Utilize that knowledge to find a solution to your problem.
 
Hello jared89, welcome to the forum

You could use the exponential function in a general form and start fitting it to the two conditions you have, however there is a slightly more advanced way. Write out the two conditions as:

[tex]f(0)=20[/tex]
[tex]f(7x)=2f(x)[/tex]

Take the derivative of the second one and use in it the original again. You will end up with a first order differential equation giving as solution the exponential function. Using the first equation as boundary gives then the function you are looking for.

Can you do this?
 

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