# Representing Exponential Functions

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The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to:

(A) determine the domain and range of exponential functions of the form *f*(*x*) = *ab ^{x}* and represent the domain and range using inequalities;

(B) interpret the meaning of the values of *a* and *b *in exponential functions of the form *f(x)* = *ab ^{x}* in real-world problems;

(C) write exponential functions in the form *f(x)* = *ab ^{x}* (where

*b*is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

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

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