Lesson 7 Logs Go Viral Practice Understanding
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
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
How many people will be infected with the virus on day
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
When does your model predict there will be
Will the number of days it will take the virus to claim
Calculate the number of days it will take for the virus to claim
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
How many zombies will there be after
How many days will it take for the zombie population to reach
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
If we start with
How long will it take for the amount of zombie goo to decay to an amount less than
When will there be no zombie goo left?
Ready for More?
Solving an exponential equation with a variable in the exponent:
Adding Notation, Vocabulary, and Conventions
The inverse of is
Natural logarithms are used to
- natural logarithm
- Bold terms are new in this lesson.
In this lesson, we modeled continuous growth and decay using the formula that is a base
How do you know that the graph of
Use the properties of logarithms and the given values to find the value of the indicated logarithm.