Interpret formulas of basic exponential functions

The  exercise appears under the Algebra I Math Mission. This exercise practices finding features of exponential functions of the basic form $$f(x)=a*r^x$$ given their formula. Features in question are the initial value, the common ratio, and output-values that correspond to various input-values.

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


 * 1) Find the values: This problem describes an exponential function and students are asked to find the initial value $$a$$ of the exponential function. Students are then asked to find for which value does $$g(x)$$ equal a certain number. Interpret formulas of basic exponential functions.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) The common ratio is a ratio of output values which have consecutive input values. Since this ratio is the same regardless of the choice of input values, it is called the common ratio.

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.