Construct basic exponential functions from the initial value and the common ratio

The  exercise appears under the Algebra I Math Mission. This exercise practices constructing exponential functions of the basic form $$f(x)=a\times r^x$$, either when given a table with two input-output pairs, or when given the graph of the function.

Types of Problems
There is one type of problem in this exercise:


 * 1) Write the formula of the function $$q(x)$$: This problem The graph below shows the value of $$q$$ with an initial value and common ratio. The student is then asked to type the formula for the function in the text box below. [[File:Construct basic exponential functions from the initial value and the common ratio.PNG|thumb|Write the formula of the function $$q(x)$$]]

Strategies
Knowledge of and experience with exponential functions are encouraged to ensure success on this exercise.
 * 1) An exponential equation is generally of the form $$f(x)=a\times b^x$$.

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.