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Limits of Exponential Functions

Everyone has their limit; logs and exponents are no different.

Let's look at the exponential function y = 4x. No matter what value of x you throw into it, though, you can never get y to be negative or zero. (How optimistic of it.) Try a few:

42, 43, 44 = 16, 64, 256


40 = 1
4-2 = 1/42 = 1/16

Sample Problem

Using the following table, pick a C and x to fit an exponential function. Hint: remember that anything to the power of 0 becomes 1.

{2,18 ; 0,2 ; 3, 56}

Because any base raised to the power of 0 equals 1, we can easily figure out the coefficient. Throw that bad boy into the mix and solve:

2 = C(b)0
2 = C(1)
C = 2

Now that you know C, use it to solve one of the other sets of variables given.

18 = 2(b)2
9 = b2

b = 3

So the exponential function we need is y = 2(3x)

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