# Standard 5: Write, solve and graph exponential and logarithmic equations and functions in one and two variables. Export Print
General Information
Number: MA.912.AR.5
Title: Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.912.AR.5.AP.2
Solve one-variable equations involving logarithms or exponential expressions. Identify any extraneous solutions.
MA.912.AR.5.AP.3
Given a real-world context, identify an exponential function as representing growth or decay.
MA.912.AR.5.AP.4
Select an exponential function to represent two quantities from a graph or a table of values.
MA.912.AR.5.AP.5
Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents.
MA.912.AR.5.AP.6
Given a table, equation or written description of an exponential function, select the graph that represents the function.
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.
MA.912.AR.5.AP.8
Given an equation of a logarithmic function, select the graph of that function.
MA.912.AR.5.AP.9
Given a mathematical and/or real-world problem that is modeled with logarithmic 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 topic.

## Formative Assessments

Interpreting Exponential Functions:

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

Type: Formative Assessment

Trees in Trouble:

Students are asked to write a function that represents an annual loss of 3 percent each year.

Type: Formative Assessment

Exponential Growth:

Students are given two functions, one represented verbally and the other by a table, and are asked to compare the rate of change in each in the context of the problem.

Type: Formative Assessment

Graphing an Exponential Function:

Students are asked to graph an exponential function and to determine if the function is an example of exponential growth or decay, describe any intercepts, and describe the end behavior of the graph.

Type: Formative Assessment

Students are asked to write and solve an equation that models an exponential relationship between two variables.

Type: Formative Assessment

Comparing Functions - Exponential:

Students are asked to use technology to graph exponential functions and then to describe the effect on the graph of changing the parameters of the function.

Type: Formative Assessment

Loss of Fir Trees:

Students are asked to sketch a graph that depicts the exponential decline in the population of fir trees in a forest.

Type: Formative Assessment

Exponential Functions - 2:

Students are asked to identify the percent rate of change of a given exponential function.

Type: Formative Assessment

Exponential Functions - 1:

Students are asked to identify the percent rate of change of a given exponential function.

Type: Formative Assessment

Case In Point:

Students are asked to explain the relationship between the set of solutions and the graph of an exponential equation.

Type: Formative Assessment

What Is the Function Rule?:

Students are asked to write function rules for sequences given tables of values.

Type: Formative Assessment

Writing an Exponential Function From a Table:

Students are asked to write an exponential function represented by a table of values.

Type: Formative Assessment

Writing an Exponential Function From a Description:

Students are asked to write an exponential function from a written description of an exponential relationship.

Type: Formative Assessment

Writing an Exponential Function From Its Graph:

Students are asked to write an exponential function given its graph.

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

Creating Exponential Functions:

Follow as we construct an exponential function from a graph, from a table of values, and from a description of a relationship in the real world in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Problem Solving with Project Constraints:

It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Asymptotic Behavior in Shark Growth Research:

Fishery Scientist from Florida State University discusses his new research in deep sea sharks and the unusual behavior that is found when the data is graphed.

Type: Perspectives Video: Professional/Enthusiast

Making Candy: Illuminating Exponential Growth:

No need to sugar coat it: making candy involves math and muscles. Learn how light refraction and exponential growth help make candy colors just right!

Type: 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]

Type: Perspectives Video: Professional/Enthusiast

## Tutorial

Graphing Exponential Equations:

This tutorial will help you to learn about exponential functions by graphing various equations representing exponential growth and decay.

Type: Tutorial

## Student Resources

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

## 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

Creating Exponential Functions:

Follow as we construct an exponential function from a graph, from a table of values, and from a description of a relationship in the real world in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Problem Solving with Project Constraints:

It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Making Candy: Illuminating Exponential Growth:

No need to sugar coat it: making candy involves math and muscles. Learn how light refraction and exponential growth help make candy colors just right!

Type: Perspectives Video: Professional/Enthusiast

## Tutorial

Graphing Exponential Equations:

This tutorial will help you to learn about exponential functions by graphing various equations representing exponential growth and decay.

Type: Tutorial

## Parent Resources

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

## Perspectives Video: Expert

Problem Solving with Project Constraints:

It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Making Candy: Illuminating Exponential Growth:

No need to sugar coat it: making candy involves math and muscles. Learn how light refraction and exponential growth help make candy colors just right!

Type: Perspectives Video: Professional/Enthusiast