MA.912.AR.5.7

Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.

Examples

The graph of the function begin mathsize 12px style f left parenthesis t right parenthesis space equals space e to the power of 5 t plus 2 end exponent end style can be transformed into the straight line y=5t+2 by taking the natural logarithm of the function’s outputs.

Clarifications

Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; constant percent rate of change; end behavior and asymptotes. 

Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation. 

Clarification 3: Instruction includes understanding that when the logarithm of the dependent variable is taken and graphed, the exponential function will be transformed into a linear function. 

Clarification 4: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
7912120: Access Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
1200710: Mathematics for College Algebra (Specifically in versions: 2022 and beyond (current))
1209315: Mathematics for ACT and SAT (Specifically in versions: 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.AR.5.AP.7: Given a mathematical and/or real-world problem that is modeled with exponential functions, solve the mathematical problem, or select the graph using key features (in terms of context) that represents this model.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessment

Interpreting Exponential Functions:

Students are asked to interpret parameters of an exponential function in context.

Type: Formative Assessment

Lesson Plan

Which Function?:

This activity has students apply their knowledge to distinguish between numerical data that can be modeled in linear or exponential forms. Students will create mathematical models (graph, equation) that represent the data and compare these models in terms of the information they show and their limitations. Students will use the models to compute additional information to predict future outcomes and make conjectures based on these predictions.

Type: Lesson Plan

Original Student Tutorials

Exponential Functions Part 3: Decay:

Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.

Type: Original Student Tutorial

Exponential Functions Part 2: Growth:

Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.

Type: Original Student Tutorial

Exponential Functions Part 1:

Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Kites, Wind, and Speed:

Lofty ideas about kites helped power a kayak from California to Hawaii.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

MFAS Formative Assessments

Interpreting Exponential Functions:

Students are asked to interpret parameters of an exponential function in context.

Original Student Tutorials Mathematics - Grades 9-12

Exponential Functions Part 1:

Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.

Exponential Functions Part 2: Growth:

Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.

Exponential Functions Part 3: Decay:

Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Exponential Functions Part 3: Decay:

Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.

Type: Original Student Tutorial

Exponential Functions Part 2: Growth:

Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.

Type: Original Student Tutorial

Exponential Functions Part 1:

Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.

Type: Original Student Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.