Today's Learning Goal:

Use properties of exponents to rewrite exponential expressions.
Surface meaning for fractional exponents and their relationship to radicals in the context of examining an exponential function.

Reminders:

Discrete functions have distinct and separate values and are used for things that can be counted. (countable)

Continuous functions can have any value within a specific interval and values are connected. (measureable)

Domain of a function: The numbers that can be used as possible inputs

Today's Materials:

Laptop
Pencil
Binder

Please complete the Jump Start (activator). This is independent it should be silent.

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Find the missing terms in this geometric sequence:
For Root Calculator click here

Lets practice and review some exponent rules!

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Simplify:
Write answer as single variable, using (^ "Shift 6") for the exponent. NO SPACES

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Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

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Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

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Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

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Simplify:

Main Objective for today:

Students can rewrite radical and rational exponents!

Let's review some quick notes

Guided Practice

Each of the expressions can be written using either radical notation or rational exponents. Rewrite each of the given expressions in the not given form.

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Rewrite the expression in the other form.

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Rewrite the expression in the other form.

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Challenge Problem:
Rewrite this expression from radical to rational form.
Hint: simplify under the root first.

Independent Practice

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F.LE.1.a

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F.LE.1.a

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F.LE.1.a

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F.LE.1.a

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F.LE.1.a

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N.RN.2

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F.IF.2

F.LE.3

For problems 22-26, You will be making real world decisions based on data modeled in different ways.

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Based on the given infomation, write the equation that represents TCF bank's situations.
Let t(x) = the total savings at TCF
Let x = the number of years

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Based on the given infomation, write the equation that represents Wells Fargo bank's situations.
Let w(x) = the total savings
Let x = the number of years
Annual means each year

The table and graph below represent the TCF and Well Fargo savings situations.

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Which bank would you choose if you decided to only save for 10 years? Explain how you made your decision.

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Which bank would you choose if you decided to only save for 20years? Explain how you made your decision.

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Will there be an amount of time that you save the same amount in both banks? (other than the beginning)
If so, what is the number of years and how did you determine this?

(U2) Lesson 4 - "Exponents Rule!"

(U2) Lesson 4 - "Exponents Rule!"

Find the missing terms in this geometric sequence:For Root Calculator click here

Simplify: Write answer as single variable, using (^ "Shift 6") for the exponent. NO SPACES

Simplify:Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:

Rewrite the expression in the other form.

Rewrite the expression in the other form.

Challenge Problem: Rewrite this expression from radical to rational form. Hint: simplify under the root first.

Independent Practice

Based on the given infomation, write the equation that represents TCF bank's situations. Let t(x) = the total savings at TCFLet x = the number of years

Based on the given infomation, write the equation that represents Wells Fargo bank's situations. Let w(x) = the total savings Let x = the number of yearsAnnual means each year

Which bank would you choose if you decided to only save for 10 years? Explain how you made your decision.

Which bank would you choose if you decided to only save for 20years? Explain how you made your decision.

Will there be an amount of time that you save the same amount in both banks? (other than the beginning) If so, what is the number of years and how did you determine this?

Find the missing terms in this geometric sequence:For Root Calculator click here

Simplify: Write answer as single variable, using (^ "Shift 6") for the exponent. NO SPACES

Simplify:Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:

Watch me while I...What form is this written in?

Rewrite the expression in the other form.

Together let's tryWhat form is this written in?

Rewrite the expression in the other form.

Independently Try thisWhat form is this written in?

Rewrite the expression in the other form.

Challenge Problem: Rewrite this expression from radical to rational form. Hint: simplify under the root first.

Independent Practice

The function below is written in rational form, write the equivalent expression in radical form.

Which graph represents the table of f(x) below as a continuous function with a domain of all real numbers.

Use the equation to fill out the table for the given inputs then graph the data as a discrete function.

Based on the given infomation, write the equation that represents TCF bank's situations. Let t(x) = the total savings at TCFLet x = the number of years

Based on the given infomation, write the equation that represents Wells Fargo bank's situations. Let w(x) = the total savings Let x = the number of yearsAnnual means each year

Which bank would you choose if you decided to only save for 10 years? Explain how you made your decision.

Which bank would you choose if you decided to only save for 20years? Explain how you made your decision.

Will there be an amount of time that you save the same amount in both banks? (other than the beginning) If so, what is the number of years and how did you determine this?

Watch me while I...What form is this written in?

Together let's tryWhat form is this written in?

Independently Try thisWhat form is this written in?

Rewrite the expression in the other form.

The function below is written in rational form, write the equivalent expression in radical form.

Which graph represents the table of f(x) below as a continuous function with a domain of all real numbers.

Use the equation to fill out the table for the given inputs then graph the data as a discrete function.

Find the missing terms in this geometric sequence:
For Root Calculator click here

Simplify:
Write answer as single variable, using (^ "Shift 6") for the exponent. NO SPACES

Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

Challenge Problem:
Rewrite this expression from radical to rational form.
Hint: simplify under the root first.

Based on the given infomation, write the equation that represents TCF bank's situations.
Let t(x) = the total savings at TCF
Let x = the number of years

Based on the given infomation, write the equation that represents Wells Fargo bank's situations.
Let w(x) = the total savings
Let x = the number of years
Annual means each year

Will there be an amount of time that you save the same amount in both banks? (other than the beginning)
If so, what is the number of years and how did you determine this?

Find the missing terms in this geometric sequence:
For Root Calculator click here

Simplify:
Write answer as single variable, using (^ "Shift 6") for the exponent. NO SPACES

Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES

Watch me while I...
What form is this written in?

Together let's try
What form is this written in?

Independently Try this
What form is this written in?

Challenge Problem:
Rewrite this expression from radical to rational form.
Hint: simplify under the root first.

Based on the given infomation, write the equation that represents TCF bank's situations.
Let t(x) = the total savings at TCF
Let x = the number of years

Based on the given infomation, write the equation that represents Wells Fargo bank's situations.
Let w(x) = the total savings
Let x = the number of years
Annual means each year

Will there be an amount of time that you save the same amount in both banks? (other than the beginning)
If so, what is the number of years and how did you determine this?

Watch me while I...
What form is this written in?

Together let's try
What form is this written in?

Independently Try this
What form is this written in?