VIDEO: Establishing an exponential function

Find the necessary points

Are you a little afraid of the next math exam? Most of the time you can use the following rule to calculate an exponential function.

• In order to be able to calculate an exponential function, you usually need a few points on the function. These are given or can be read directly from the graph.
• in the high school the points that are given are mostly extreme values. In the second derivative, these have the y-value equal to 0, since they are tangent slope values.
• Make sure, when picking out the points, that you always have as many unknowns as Equations to have. In the following z. B. 3 equations since you have a, k and c as unknowns.

If you have now figured out the points, you can set up the exponential function.

Establish the exponential function

1. The exponential function usually has the same form: f (x) = a ^ (kx) * c. This is a general form of the exponential function. The Eulerian number is known as a special form, which is used in the
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   mathematics is abbreviated with e. f (x) = e ^ (kx).
2. Once you have found out the points as described above, they are now inserted into the equation.
3. The first derivative is f` (x) = a ^ (kx) * ln (a) * c * k. For the Eulerian function the derivative is: f '(x) = k * e ^ (kx) and for the function: f (x) = ln (x) the derivative is f' (x) = 1 / x.
4. You have now established all equations and points. Now try to solve the equations with addition and subtraction and find out the unknowns a, b, c and d.
5. Now you can set up the exponential function and fill in the unknowns. The x and the e stay in such a way that e stands for the Eulerian number and the x can vary depending on the point. Z. B. the function could look like this: f (x) = 5 ^ (3x) * 2.
6. You can check this in your calculator with the graph function or create a value table to check your function values.

Setting up the exponential function takes some practice. Repeat it a few times and you will notice that everything always follows a similar pattern.