# Lesson 7 Logs Go Viral Practice Understanding

## Learning Focus

Model continuous growth and decay using base

Solve exponential equations using natural logarithms.

How can we solve continuous growth and decay problems that are modeled using base

## Open Up the Math: Launch, Explore, Discuss

As we learned in the previous lesson, *Compounding the Problem*, when money is compounded continuously, it turns out that the base of the exponential growth function is

Continuous growth:

Continuous decay:

In both cases,

Since there are many things that grow or decay continuously in nature,

You are an epidemiologist, a person who studies the outbreak and spread of diseases. Part of your job is to help avoid a pandemic—a worldwide outbreak of a disease. You know some of the most difficult diseases to deal with are viruses because they don’t respond to many of the medicines we have available and because viruses are able to mutate and change quickly, making it more difficult to contain them. You have been studying a new virus that causes people to break out in spots. Suddenly, a colleague rushes into your office to inform you there is a confirmed outbreak of the virus in Europe. The growth of the virus through a population is continuous (until it is somehow contained) at a rate of

### 1.

How many people will be infected with the virus on day

### 2.

Create a model of the spread of the spotted virus in this region if it is not contained. To simplify your model slightly, consider the

Table:

Equation:

### 3.

When does your model predict there will be

### 4.

Will the number of days it will take the virus to claim

### 5.

Calculate the number of days it will take for the virus to claim

### 6.

On what day will there be

Now you have received a report of a mysterious illness that seems to turn the infected humans into mindless zombies has broken out in a major American city. Since the hungry zombies prey upon innocent people, the outbreak grows continuously at a rate of

### 7.

How many zombies will there be after

### 8.

How many days will it take for the zombie population to reach

### 9.

At what rate would the zombie population be growing if it reached

Now we’re going to get a little more far-fetched in the scenario. Let’s say that zombies produce radioactive goo that decays continuously with a half-life of

### 10.

If we start with

### 11.

How long will it take for the amount of zombie goo to decay to an amount less than

### 12.

When will there be no zombie goo left?

## Ready for More?

Graph

## Takeaways

Solving an exponential equation with a variable in the exponent:

## Adding Notation, Vocabulary, and Conventions

The inverse of is

Natural logarithms are used to

## Vocabulary

- natural logarithm
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we modeled continuous growth and decay using the formula that is a base

### 1.

How do you know that the graph of

### 2.

Use the properties of logarithms and the given values to find the value of the indicated logarithm.

Given:

Find: