AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

Last updated over 4 years ago

19 questions

AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

Last updated over 4 years ago

19 questions

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible.

You were likely unable to write the equation for the last two tables.  They are exponential functions.  In AA3-3, we will study graphing exponential functions in the form:  
However, for now, we will write exponential functions centered at the origin so (h,k) is (0,0).  As a result, we will write exponential functions in the form: 
                                    -- a is the starting value  (f(0))
                                    -- b is the rate of growth or decay (what we are multiplying by each time)
                                    -- x is the number of times something occurs.  It is often, but not always, an amount of time.  

Because f(x) increases as x increases, this function is a model of exponential growth.
Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.
Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Predict whether f(x) = 1/2 (5)x is a model for exponential growth or decay?

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

How do you know if an exponential function will model growth or decay?

Draggable item		Corresponding Item

Draggable item		Corresponding Item
neither		f(x)=8(1.7)x
neither		f(x)=8(0.7)x
growth		f(x)=8(1/4)x
growth		f(x)=1/4(8)x
decay		f(x)=8(0)x
growth		f(x)=8(1)x
decay		f(x)=1(8)x

AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible.

Because f(x) increases as x increases, this function is a model of exponential growth.
Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.
Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Predict whether f(x) = 1/2 (5)x is a model for exponential growth or decay?

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

How do you know if an exponential function will model growth or decay?

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible.

Because f(x) increases as x increases, this function is a model of exponential growth.
Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.
Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Is f(x) = 4(3)x a model for exponential growth or decay?

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Is f(x) = 4(0.75)x a model for exponential growth or decay?

Predict whether f(x) = 1/2 (5)x is a model for exponential growth or decay?

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Is f(x) = 1/2 (5)x is a model for exponential growth or decay?

How do you know if an exponential function will model growth or decay?

Match each exponential function:

AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible.

Because f(x) increases as x increases, this function is a model of exponential growth.Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3). Don't forget (anything)0 = 1.Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3). Don't forget (anything)0 = 1. Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Predict whether f(x) = 1/2 (5)x is a model for exponential growth or decay?

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3). Don't forget (anything)0 = 1. Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

How do you know if an exponential function will model growth or decay?

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write an equation for f(x)

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible

Describe what is happening to f(x) as x increases:

Write the equation of f(x), if possible.

Because f(x) increases as x increases, this function is a model of exponential growth.Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3). Don't forget (anything)0 = 1.Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Is f(x) = 4(3)x a model for exponential growth or decay?

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3). Don't forget (anything)0 = 1. Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Is f(x) = 4(0.75)x a model for exponential growth or decay?

Predict whether f(x) = 1/2 (5)x is a model for exponential growth or decay?

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3). Don't forget (anything)0 = 1. Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Is f(x) = 1/2 (5)x is a model for exponential growth or decay?

How do you know if an exponential function will model growth or decay?

Match each exponential function:

Because f(x) increases as x increases, this function is a model of exponential growth.
Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.
Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Because f(x) increases as x increases, this function is a model of exponential growth.
Write the exponential equation for this table:

Because f(x) decreases as x increases, this function is a model of exponential decay.
Write the exponential equation for this table:

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.