# Unit 5Exponential and Logarithmic Functions

## Lesson 1

### Learning Focus

Find exact and estimated values of logarithms.

### Lesson Summary

In this lesson, we found exact and approximate values for logarithmic expressions. We drew conclusions about properties of logarithms that are always true. We also identified characteristics of logarithmic functions that will help us to graph logarithms in the next lesson.

## Lesson 2

### Learning Focus

Identify and explain common features of the graphs of exponential functions.

Identify and explain common features of the graphs of logarithmic functions.

Transform the graph of an exponential or logarithmic function.

### Lesson Summary

In this lesson, we graphed exponential and logarithmic functions by hand and used technology to determine common features in the graphs. We used technology to identify how the transformations appear in the equations of exponential functions. We examined graphs and wrote equations for the transformed functions, and we graphed transformed functions given the equations.

## Lesson 3

### Learning Focus

Model the growth of an invasive species.

Explain why exponential functions are good models for unchecked population growth.

Relate expressions with rational exponents to the growth of a population.

### Lesson Summary

In this lesson, we learned how to change the form of exponential functions to reflect different rates of growth over different intervals of time. We used the rules of exponents to make equivalent functions. We interpreted exponential expressions in terms of a context by interpreting both the base of the expression and the exponent.

## Lesson 4

### Learning Focus

Use logarithms to solve exponential equations.

Solve systems of equations that contain exponential functions.

### Lesson Summary

In this lesson, we found solutions to base exponential equations by using base logarithms to undo the equation. We used tables and graphs to help support our thinking about whether the solutions we find are reasonable. We solved systems of equations both by finding the intersection of the graphs and by finding the value that makes both equations true.

## Lesson 5

### Learning Focus

Model the growth of a savings account earning compound interest.

Solve exponential equations using logarithms.

### Lesson Summary

In this lesson, we modeled the growth of a savings account earning compound interest with an exponential function. We interpreted the compound interest formula to understand how it changes when the number of compounding periods each year is changed. We learned to use logarithms to solve exponential equations of any base when the variable is in the exponent.