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Day 88 – simple and compound interest
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Word Problem In this activity, you will explore the values of the expressions 3x and 3x as x changes from 0 to 5. You will compare the two expressions by investigating patterns in how their values change both in a table and graphically.
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1. Complete the table below. Which column is growing faster?
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2. a. As x increases from 2 to 3 in the table, how does the value of 3x change? b. As x increases by 1, describe the pattern in the numbers in the 3x column of the table. 3. a. As x increases from 2 to 3 in the table, how does the value of 3x change? b. As x increases from 3 to 4 in the table, how does the value of 3x change? c.As x increases by 1, describe the pattern you notice in the numbers in the 3x column of the table.
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4. Graph the points in Desmos. Compare the two graphs 5
4. Graph the points in Desmos. Compare the two graphs 5. What is the domain when the values for 3x increasing faster than the values for 3x?
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6. Aaron says that the values of f(x) = 5x will increase faster than the values of the linear function f(x) = 5x. Do you agree or disagree? Support your answer. Define the domain where this is true. Define the domain where this is false.
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Answer Key 1. Complete the table below. Which column is growing faster?
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2. a. As x increases from 2 to 3 in the table, how does the value of 3x change? Increases by 3 b. As x increases by 1, describe the pattern in the numbers in the 3x column of the table. you can add 3 each time 3. a. As x increases from 2 to 3 in the table, how does the value of 3x change? multiplied by 3, goes up by 18 b. As x increases from 3 to 4 in the table, how does the value of 3x change? multiplied by 3, goes up by 54 c. As x increases by 1, describe the pattern you notice in the numbers in the 3x column of the table. multiplied by 3
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4. Graph the points in Desmos. Compare the two graphs
5. What is the domain when the values for 3x increasing faster than the values for 3x? x > 1
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6. Aaron says that the values of f(x) = 5x will increase faster than the values of the linear function f(x) = 5x. Do you agree or disagree? Support your answer. answer will vary Define the domain where this is true. x > 1 Define the domain where this is false. x ≤ 1
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