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

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To create a function that starts at 20 and triples every 7, one can utilize the concept of exponential functions. The conditions can be expressed mathematically as f(0)=20 and f(7x)=2f(x). By taking the derivative of the second condition and substituting it into the first, a first-order differential equation is derived, leading to an exponential function solution. Applying the boundary condition from the first equation will yield the desired function. This approach effectively combines calculus with exponential growth principles.
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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:

f(0)=20
f(7x)=2f(x)

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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