Modeling with exponential functions

The  exercise appears under the Algebra II Math Mission. This exercise increases experience with word problems and modeling, specifically with exponential models.

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


 * 1) Find the model and answer the questions: This problem describes a real-life situation. The student is asked to use the description to find a model and use it to answer some related questions.Mwef1.png
 * 2) Answer the question using the model: This problem gives an exponential model. The student is supposed to use the given model to answer a question based on the situation.Mwef2.png

Strategies
Knowledge of and experience with exponents and logarithms are encouraged to ensure success on this exercise.
 * 1) An exponential equation is generally of the form $$f(x)=a\times b^x$$.
 * 2) With word problems, plugging in information can help to answer the question more 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) Many of the problems in this exercise are application word problems.