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 theJump Start (activator). This is independent it should be silent.
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Question 1
1.
Find the missing terms in this geometric sequence:
For Root Calculator click here
Lets practice and review some exponent rules!
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Question 2
2.
Simplify:
Write answer as single variable, using (^ "Shift 6") for the exponent. NO SPACES
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Question 3
3.
Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES
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Question 4
4.
Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES
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Question 5
5.
Simplify:
Write answer as single variable, using ^ for the exponent. NO SPACES
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Question 6
6.
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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Question 7
7.
Watch me while I...
What form is this written in?
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Question 8
8.
Rewrite the expression in the other form.
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Question 9
9.
Together let's try
What form is this written in?
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Question 10
10.
Rewrite the expression in the other form.
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Question 11
11.
Independently Try this
What form is this written in?
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Question 12
12.
Rewrite the expression in the other form.
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Question 13
13.
Challenge Problem:
Rewrite this expression from radical to rational form.
Hint: simplify under the root first.
Independent Practice
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Question 14
14.
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Question 15
15.
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Question 16
16.
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Question 17
17.
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Question 18
18.
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Question 19
19.
The function below is written in rational form, write the equivalent expression in radical form.
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Question 20
20.
Which graph represents the table of f(x) below as a continuous function with a domain of all real numbers.
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Question 21
21.
Use the equation to fill out the table for the given inputs then graph the data as a discrete function.
For problems 22-26, You will be making real world decisions based on data modeled in different ways.
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Question 22
22.
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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Question 23
23.
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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Question 24
24.
Which bank would you choose if you decided to only save for 10 years? Explain how you made your decision.
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Question 25
25.
Which bank would you choose if you decided to only save for 20years? Explain how you made your decision.
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Question 26
26.
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?
