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# Exponential Functions - Problem 5

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

A typical problem with exponential functions is, finding the equation of an exponential function that fits certain situations. Here I have an example of a problem like this; find an exponential function f of x equals a times b to the x such that, f of x plus 3 over f of x equals 10 and f of 0 equals 5.

So the first thing you want to do is set this up. Finding an exponential function means finding the a and b values. So you want to set these up using information they give you about f of x plus 3 and f of x. And so f of x plus 3, over f of x is 8 times b to the x plus 3 over f of x is, a times b to the x. A lot of this is going to cancel. A cancels, b to the x plus 3, is b to the x times b to the 3. Find the product of powers property, and so we can see that b to the x is going to cancel as well. So f of x plus 3 over f of x equals 10, what I just discovered is that bq equals 10. Therefore b is a cube root of 10.

Now I just need to find a. I’m going to use this fact here, f of 0 equals 5. F of 0 is a times b to the 0 being the 0 is 1, so a equals 5. And that’s it.

My function is 5 times the base cube root of 10 to the x, a times b to the x.

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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

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