Compare the growth rates of exponentials and polynomials

The  exercise appears under the Algebra II Math Mission. This exercise

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine which model is greater at different times: This problem has two models, one polynomial and one exponential, represented as a graph or a table. The student is asked to determine which model takes on greater values at different times.Cgroeap1.png

Strategies
An ability to plug in values and interpret graphs and tables are encouraged to ensure success on this exercise.
 * 1) In the short run a polynomial can exceed an exponential, but long run the exponential will exceed all polynomials.
 * 2) Research indicates the answer to the first problem is the polynomial, the answer to the second is the exponential, and the third answer is the one that indicates that exponential growth exceed polynomial growth.

Real-life Applications

 * 1) An ability to compare times is useful in theoretical computer science.
 * 2) Comparison between these types of growth are useful in finance as simple and compound interest.