Learning Goals: (1)Create a need for the formula(2)Understand that exponential functions have a multiplying rate of change (3)Provide a context for the meaning of a and b.

HSF.LE.A.1 – Distinguish between situations that can be modeled with linear functions and with exponential functions.

HSF.LE.A.2 – Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

HSF.LE.B.5 – Interpret the parameters in a linear or exponential function in terms of a context.

TEKS (2015-16)

A.9(A) – determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities

A.9(B) – interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems

A.9(C) – write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

A.9(D) – graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems

A.9(E) – write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems