This week wasn’t so bad for me, and some of the only problems that I really had were with exponential growth and decay. Logs and exponent properties seem quite easy, and the word problems are easy to pick out the information you need quickly. Something that I feel that I’ve just gotten is Exponential Functions, so I’m going to try to expain it to you:
Formula Needed: f(x) = ab^x
Goal: Use the functions to find the value of the exponential function so that you have a formula to show the relation of change in the solution to the change in the x value.
A is the value of your first function, typically f(0) = a
B is the value you need to find. It is raised to the x value.
Example:
Find an exponential function if: f(0) = 3, f(1) = 15
1. Remember the formula: f(x) = ab^x
2. Let’ s start with f(0) = 3
3. Raise b to the x power: f(0) = ab^0
4. Since x is equal to zero, b is canceled leaving you with: f(0) = a
5. Therefore, a=3
6. Continue with the second part: f(1) = 15
7. Plug in the a value from the first part and raise b to the x value: f(1) = (3)b^1
8. 3b^1 = 15, So, b = 5.
9. Replace the x values with the variable, x: f(x) = (3)(5)^x
