Alg1 Lesson 4.5: Modeling with Exponential Functions

Lesson 4.5: Modeling

with Exponential

Functions

Obj: 9B, 9C, 9D, 9E: I can approximate input and
output values of an exponential function and model a contextual scenario with an exponential function.

EQ: How can I use exponential function models to
make predictions of a given scenario?

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Roles:
Facilitator
Scribe
Resourcer
Includer

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

Which of the following have you done most this year?

• Facilitator

• Scribe

• Resourcer

• Includer

• I still don't like working in groups, although I know it is necessary sometimes.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Modeling

Depreciation

Inflation (What if you had $1,000?)

Have you noticed that prices seem to increase over
time? This is called inflation. The Federal Reserve
tries to keep inflation constantly increasing, because
a slowly increasing price level keeps businesses
profitable. A different way to describe inflation is that
the buying power of your money decreases a little bit
every year. In recent times, money has been worth
about 97% of what it was worth the previous year.

Multiple Choice

If every year money keeps 97% of its worth, how much will your $1,000 be worth in
1 year?

• $970
• $800
• $1,030

• $1,000

Fill in the Blanks

What about the year after that? If every year money keeps 97% of its worth, how much will your $1,000 be worth in 2 years?

Word Cloud

What is your opinion on inflation in a few words?

Years

Value

Dropdown

This is ​

Select answer

function since there is a common ​

Select answer

between successive years. To get the value of the money, you ​

Select answer

0.97.

Multiple Choice

Which function models this?

• V(t) = 1000 * (0.97)^t
• V(t) = 1000 * (0.99)^t
• V(t) = 1000 * (0.95)^t

Fill in the Blanks

$V\left(t\right)=1000\left(0.97\right)^t$

How much money would $1,000 be worth in 10 years according to the model?

Multiple Choice

$$V\left(t\right)=1000\left(0.97\right)^t$$

Suppose we want to know approximately how many years it would take for the original $1,000 to be worth half as much. We need to know what input value will give an output of $500. We can use guess and check or we can look at a graph. As the graph shown indicates, it would take approximately how many years for the value to depreciate to $500?

• 23 years

• 50 years

• 20 years

• 14 years

• 16 years

Multiple Choice

Which is the correct answer?

• A.

• B.

• C.

• D.

Part 2: Modeling Copying

Genes

Part 3: Summary and

Practice

Key Ideas to write in journal

●

The algebraic form of an exponential function is f(x) = a(B)^x,
where (0, a) is the coordinate of the y-intercept and B is the
common ratio.

●

When the value of B is greater than 1, it is an exponential
growth function. When the value of B is less than 1 but greater
than 0, it is an exponential decay function

●

Exponential functions grow by equal factors over equal
intervals.

●

One half of the graph of an exponential function will approach
the x-axis, while the other side gets farther away from the x-axis.

●

Exponential functions are a good choice to model scenarios
where there is a percent change.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin
the wheel as a class and spend a minute or so
discussing our answers.