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# Exponential Growth and Interest Day 2 of 2

Lesson 11 of 15

## Objective: Students will be able to build the interest formula and use it to model situations involving interest.

*50 minutes*

#### Warm Up and Homework Review

*10 min*

I include **Warm ups** with a Rubric as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up - Exponential Growth Interest Day 2 asks students to determine at what interest rate $1000 becomes $2000 given 10 years.

I also use this time to correct and record the previous day's Homework.

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This is the second day of a two day lesson. In the previous lesson, the students began to build the compound interest formula. Each class will have progressed at different rates and will pick up where they left off. This activity is the key to the entire lesson and students should be given enough time to grapple with it with out interference (**Math Practice 1**). Please see the narrative for the previous lesson for detailed instructional plans.

#### Resources

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#### Guided Practice

*27 min*

The remainder of the lesson includes a Guided Practice of Interest Problems based on the formula that the students finished writing. I have included three examples. I may make up additional problems if I observe that my students need more practice.

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to use write a function to model an interest scenario.

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The assignment has students practice the skills learned in class first by finding and using a interest function based on an annually compounding interest rate. It then has the student take the same problem but change it to compounding quarterly and then monthly. They will also use the interest function to find how long it takes an investment to double. Finally, they will determine which of two possible interest rates is the best deal. This problem may need scaffolding as there is no initial investment given. Depending on your students, you may want to forewarn them about this problem and brainstorm possible methods of solving before they leave class.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: Exponential Models Day 1 of 2
- LESSON 4: Exponential Models Day 2 of 2
- LESSON 5: Exponential Functions
- LESSON 6: Exponential Decay Functions
- LESSON 7: Simplifying Logarithms
- LESSON 8: Exponential and Logarithmic Equations
- LESSON 9: Logarithmic Functions
- LESSON 10: Exponential Growth and Interest Day 1 of 2
- LESSON 11: Exponential Growth and Interest Day 2 of 2
- LESSON 12: Natural Logarithms
- LESSON 13: Exponential and Logarithmic Functions Review Day 1
- LESSON 14: Exponential and Logarithmic Functions Review Day 2
- LESSON 15: Exponential and Logarithmic Functions Test