Construct basic exponential functions from a table or a graph

The  exercise appears under the Algebra II 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: This problem The graph below shows the exponential function $$h(x)$$ in the form $$h(x)=a\times r^x (r>0)$$. The student is asked to write a model for both situation, one which is exponential and one which is linear. After doing so, they answer a question based on the models.Construct basic exponential functions from a table or a graph.PNG

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.
 * 4) Some of the problems in this exercise are application word problems.