| Distinguish between linear and exponential models | |
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| Description | |
| Exercise Name: | Distinguish between linear and exponential models |
| Math Missions: | Algebra I Math Mission, Mathematics II Math Mission Precalculus Math Mission, Mathematics III Math Mission |
| Types of Problems: | 2 |
The Distinguish between linear and exponential models exercise appears under the Algebra I Math Mission, Mathematics II Math Mission, Precalculus Math Mission and Mathematics III Math Mission. This exercise explores the properties and differences between linear and exponential growth and decay.
Types of Problems[]
There are two types of problems in this exercise:
- 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.
Determine why model is of particular type
- 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.
Determine types of models
Strategies[]
Knowledge of linear and exponential relationships and how they effect formulas is necessary to complete this exercise accurately and efficiently.
- 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.
- Exponential models grow by a multiplication factor, so the word "factor" is often an indicator of exponential growth.
- 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.
- Exponents are used in Computer Game Physics, pH and Richter Measuring Scales, Science, Engineering, Economics, Accounting, Finance, and many other disciplines.
- Exponential Growth is a critically important aspect of Finance, Demographics, Biology, Economics, Resources, Electronics and many other areas.
- Exponential Decay is associated with Light, Sound, Sporting Fixtures, Dangerous Chemicals, and Radioactive Waste.
- Careers that use Exponents include Economists, Bankers, Financial Advisors, Insurance Risk Assessors, Biologists, Engineers, Computer Programmers, Chemists, Physicists, Geographers, Sound Engineers, Statisticians, Mathematicians, Geologists and many other professions.
Real-life Applications[]
- Exponential models are used in business for compound interest and linear can represent simple interest.
- Population growth, at least at the beginning, is exponential.
- These concepts are related to arithmetic (linear) and geometric (exponential) sequences and series which have applications in calculus.