**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.)

**Grade:**912

**Strand:**Algebraic Reasoning

## Related Benchmarks

## Related Access Points

## Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Tutorial

## Student Resources

## Original Student Tutorials

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

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

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

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

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

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

## Problem-Solving Tasks

In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.

Type: Problem-Solving Task

This problem solving task challenges students to find the linear, exponential and quadratic functions based on two points.

Type: Problem-Solving Task

This problem solving task asks students to solve five exponential and linear function problems based on a US population chart for the years 1790-1860.

Type: Problem-Solving Task

This problem solving tasks asks students to find the values of points on a graph.

Type: Problem-Solving Task

This problem solving task asks students to graph a function and find the values of points on a graph.

Type: Problem-Solving Task

The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year. There is an opportunity for further discussion based on part (c), since the ratio of costs from one year to the next is the same in each part.

Type: Problem-Solving Task

This problem is an exponential function example that uses the real-world problem of how fast rumors spread.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills. In particular, students are introduced to the idea of inflation of prices of a single commodity, and are given a very brief introduction to the notion of the Consumer Price Index for measuring inflation of a body of goods.

Type: Problem-Solving Task

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Type: Problem-Solving Task

## Tutorial

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

Type: Tutorial

## Parent Resources

## Perspectives Video: Expert

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

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

## Problem-Solving Tasks

In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.

Type: Problem-Solving Task

This problem solving task challenges students to find the linear, exponential and quadratic functions based on two points.

Type: Problem-Solving Task

This problem solving task asks students to solve five exponential and linear function problems based on a US population chart for the years 1790-1860.

Type: Problem-Solving Task

This problem solving tasks asks students to find the values of points on a graph.

Type: Problem-Solving Task

This problem solving task asks students to graph a function and find the values of points on a graph.

Type: Problem-Solving Task

The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year. There is an opportunity for further discussion based on part (c), since the ratio of costs from one year to the next is the same in each part.

Type: Problem-Solving Task

This problem is an exponential function example that uses the real-world problem of how fast rumors spread.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills. In particular, students are introduced to the idea of inflation of prices of a single commodity, and are given a very brief introduction to the notion of the Consumer Price Index for measuring inflation of a body of goods.

Type: Problem-Solving Task

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Type: Problem-Solving Task