# Exponents and Exponential Functions

## Objective

Write exponential growth functions to model financial applications, including compound interest.

## Common Core Standards

### Core Standards

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• F.IF.C.8.B — Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01 12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

• F.LE.A.2 — Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

• F.LE.B.5 — Interpret the parameters in a linear or exponential function in terms of a context.

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• 7.RP.A.3

## Criteria for Success

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1. Identify the percent change in exponential growth functions.
2. Understand the difference between simple interest (linear growth) and compound interest (exponential growth).
3. Understand that where compounding happens more frequently, the growth rate will be higher.
4. Write and evaluate exponential functions for compound interest situations and compare to simple interest situations.

## Anchor Problems

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### Problem 1

Act 1:

a. Watch the video of Act 1 of “Fry’s Bank.”

b. How much money do you think Fry has in his bank account now? Make a guess that is too low. Make a guess that is too high.

Act 2:

c. What information do you need to know about Fry’s account to determine exactly how much he has in his account now?

Act 3:

d. Watch the video of Act 3.

e. Are you surprised?

f. Do you think Fry’s account earned interest in a linear growth model or an exponential growth model?

g. What equation do you think models this?

#### References

Dan Meyer's Three-Act Math Fry's Bank

### Problem 2

Consider the three situations below.

Situation A: You invest $1,000 for 5 years at a simple annual interest rate of 4.8%. Situation B: You invest$1,000 for 5 years at an interest rate of 4.8% compounded annually.

Situation C: You invest 1,000 for 5 years at an interest rate of 4.8% compounded monthly. a. Determine how much money you would have in your account in each situation. Assume you make neither deposits nor withdrawals. b. Determine how much you would have in your account in each situation if you invested for 25 years instead of 5 years. c. Under what circumstances will your investment earn the most interest? #### Guiding Questions Create a free account or sign in to access the Guiding Questions for this Anchor Problem. ## Problem Set ? The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set. ## Target Task ? 1. A youth group has a yard sale to raise money for a charity. The group earns800 but decides to put its money in the bank for a while. The group considers two different banks:

• Cool Bank pays simple interest at a rate of 4%, and the youth group plans to leave the money in the bank for 3 years.
• Hot Bank pays an interest rate of 3% compounded annually, and the youth group plans to leave the money in the bank for 5 years.

Write a function to represent the amount of money earned at each bank. Then determine how much money the youth group would earn in each situation.

2. If the youth group needs the money quickly, which is the better choice? Explain your reasoning.