2/29 - Exponential Regression

​Remove Your
Hoodie

Put up ALL
headphones/ earbuds

Prepare to Relinquish your cellphone until the end of class.

Math Response

WARM UP:

What is the linear equation that best fits the given data?

Type answer here

Correct Answer: y=0.433x+14.7

Deg^°

Rad

LO: SWBAT use technology to determine a function
model using the exponential regression and use
regression equations to make predictions.

DOL: Given 5 problems, students will correctly use
technology to determine a function model using the
exponential regression and use regression equations to make predictions in at least 4 of 5 questions.

7

ALGI.9E - Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

9

Exponential function

Form y = ab^x

Horizontal asymptote

Exponential growth
-Nonlinear increase
of form b^x (b > 1)

Exponential decay
-Nonlinear decrease
of form b^x (0 < b < 1)

Curve of Best Fit

Exponential Regression

The curve that best shows the

trend of a given data set

The mathematical process of calculating the

curve of best fit

Lesson Vocabulary

9

Today you will write the
exponential function that
best fits a table of values.

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Line of Best Fit

Linear

Function

Quadratic Function

Multiple Choice

Which of the following exponential equations best fits the data below?

• $$y=330\left(1.07\right)^x$$

• $$y=330\left(1.09\right)^x$$

• $$y=350\left(1.07\right)^x$$

• $$y=350\left(1.09\right)^x$$

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No Choice

Harmen, a worker for the census bureau, suspects that the population of a certain
town is growing exponentially. He wants to present his theory to his supervisor
but needs more evidence to support it.

Years since 2017

Population

0

9,400

1

9,900

2

10,500

3

11,300

4

12,000

5

12,700

6

13,700

Write an exponential equation that
Harmen can use to model the town’s
population growth.

What if there are no answer

choices to test?

We will use a calculator process called

Exponential Regression.

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Now Desmos will calculate the exponential curve of best fit.

Refresher: Regressions in Desmos

But wait!

There is one more thing.

15

Desmos has an extra little feature for exponential regressions that it doesn’t
have for linear or quadratic regressions.

Exponential Regressions in Desmos

Do you see it?

It’s called Log Mode.

Desmos has a unique way of
performing regressions that
other graphing calculators
don’t use.

Long story short:

Check the box.

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Desmos has now (correctly) calculated the exponential curve of best fit.

Now note the list of variables.

a =
b =

What is the equation?

Exponential Regressions in Desmos

Multiple Choice

Which equation best fits the data of the exponential function shown.

• $$y=0.2\left(1.25\right)^x$$

• $$y=0.2\left(1.5\right)^x$$

• $$y=0.1\left(1.25\right)^x$$

• $$y=0.1\left(1.5\right)^x$$

17

Predicting with
Exponential Regression

Using the equation found in the previous question. What would be the value of y is the x-coordinate was 12?

Math Response

Determine the exponential function that best fits the given data.

Type answer here

Correct Answer: y=0.42\left(1.31\right)^x

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Rad

Labeling

Using the equation of exponential function $$y=0.42\left(1.31\right)^x$$ what is the value missing value from the table

Drag labels to their correct position on the image

2.4

6

1.7

2.1

1.8

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Franco is a cattle rancher who has been trying
to expand his cattle population. He has kept the following data on the number of cows he has over the past several years.

Practice

Year (x)Number of cows (y)

2017

1,750

2018

1,809

2019

1,875

2020

1,956

2021

2,010

2022

2,077

2023

2,146

2024

2,227

At what percentage rate has the cattle population been increasing on Franco’s ranch each year?

Longhorn Cattle by TheWriteReflection from Pixabay

​When looking at years, DO NOT enter the years as your x-values. Instead enter the number of years.

​You have 3 minutes to discuss with your shoulder partner on should you start counting at 0 or 1.

Math Response

Franco is a cattle rancher who has been trying to expand his cattle population. He has kept the following data on the number of cows he has over the past several years.

At what percentage rate has the cattle population been increasing on Franco's ranch each year?

Type answer here

Correct Answer: 3.5

Deg^°

Rad

Math Response

A certain substance in a laboratory is accidentally exposed to a reagent and starts to decay. However, this goes on for some time before it is noticed. Once the lab scientists notice what is happening, they decide to carefully measure the remainder of this phenomenon until the substance has completely decayed.

About how many grams of the substance were initially exposed to the reagent?

Type answer here

Correct Answer: 11600

Deg^°

Rad

Dropdown

Javier opened a CD account with his local bank 3 years ago. He deposited $5,000 and agreed to leave the money in the account for 10 years without making any withdrawals. The table shows how his account balance has changed in 3 years. The initial value of $ ​

Select answer

​ will grow at a rate of ​

Select answer

making his balance at the end of the 10 years $

Select answer

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Recap

●We can plot data tables and graphs
together on the same set of axes.

●If the curve follows the data points very closely, we have a good fit.

●We can use exponential regression to generate a curve of best fit.

●With regression, an r-value close to 1
means we have strong correlation
(a good fit).

DOL: Given 5
problems, students
will correctly use
technology to
determine a
function model
using the
exponential
regression and use
regression
equations to make
predictions in at
least 4 of 5
questions.

25

Demonstration of Learning

Open Ended

How can we tell when an exponential equation is a good fit for a data table?

Use complete sentence: When looking at an exponential equation graph you can tell if it is a good fit to the data if...