1. Day 88 – simple and compound interest

2. 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.

3. 1. Complete the table below. Which column is growing faster?

4. 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.

5. 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?

6. 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.

7. Answer Key
1. Complete the table below. Which column is growing faster?

8. 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

9. 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

10. 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