Constructing linear and exponential functions

The  exercise appears under the Algebra II Math Mission. This exercise practices creation of linear and exponential models of data and of situations.

Types of Problems
There are two types of problems in this exercise:


 * 1) Describe the algebraic models and apply them: This problem describes some growth situations. The student is asked to write a model for both situation, one which is exponential and one which is linear. After doing so, they answer a question based on the models.Claef1.png
 * 2) Find the models from the values: This problem provides a T-table with several inputs and outputs. The student is expected to create a model for each function based on the table.Claef2.png

Strategies
Knowledge of and experience with exponents and logarithms are encouraged to ensure success on this exercise.
 * 1) A linear equation is of the form $$f(x)=mx+b$$.
 * 2) An exponential equation is generally of the form $$f(x)=a\times b^x$$.
 * 3) A TI-83/84 calculator can use a STAT option to create models quickly, if values can be inserted into the calculator efficiently.

Real-life Applications

 * 1) Practice with logarithms increase ability with exponents.
 * 2) Logarithms are useful in many scales, such as Richter, Decibel and pH.
 * 3) Exponentials can be used to model things that grow by a relative rate, for example, compound interest and population.
 * 4) Some of the problems in this exercise are application word problems.