Distinguish between linear and exponential models

The  exercise appears under the Algebra I Math Mission, Algebra II Math Mission and Precalculus Math Mission. This exercise explores the properties and differences between linear and exponential growth and decay.

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


 * 1) Determine why model is of particular type: This problem provides the description of a growth or decay model. The student is asked to determine which type of model it is and the reason for this answer.Ulaem1.png
 * 2) Determine types of models: This problem provide a bubble chart with four different models. The student is asked to determine whether each model is linear or exponential.Ulaem2.png

Strategies
Knowledge of linear and exponential relationships and how they effect formulas is necessary to complete this exercise accurately and efficiently.
 * 1) The answer in the first problem type will always involve a reason with numbers. An answer choice without referring to the factor or amount is not going to be correct.
 * 2) Exponential models grow by a multiplication factor, so the word "factor" is often an indicator of exponential growth.
 * 3) Linear models grow by a constant amount that does not change in absolute amount, whereas exponential models grow by relative amounts and so the absolute amounts will change.

Real-life Applications

 * 1) Exponential models are used in business for compound interest and linear can represent simple interest.
 * 2) Population growth, at least at the beginning, is exponential.
 * 3) These concepts are related to arithmetic (linear) and geometric (exponential) sequences and series which have applications in the calculus.