# Exploring linear and exponential growth

**Question description**

You and some friends have started your own company. After the first few months, the profits are rolling in. It is time to start thinking about putting your money to work for you. You decide that investing $5,000 into some Certificates of Deposit (CDs) would be a beneficial move.

With a CD, you lend your money to a third party, and after a set time, your money is paid back with interest. Before you start investing the company's money this way, you need to pitch it to your friends.

For this project, you can develop a written report, a slideshow, a video, or any other platform as long as it fully addresses the criteria listed below.

- Research the highest interest rate (APY—annual percent yield) for 2-year and 5-year CDs. Document the company's name, interest rate, and minimum investment. The minimum investment must be less than or equal to $5,000.
- Create the functions that represent the 2-year and 5-year CDs with your $5,000 investment. Use these functions to determine the amount you will be paid when the CD matures (the length of time for the specific CD). Show your work.
- An investor comes to your office. He says that if you give him the $5,000, he will add on an additional $50 each year to what he owes you. Create the function for this investor's plan.
- Create a table showing the value of the two CDs and the investor's plan for 5 years.

5. Explain to your friends how to prove that the investor's plan is a linear function and the CDs are exponential functions. Use complete sentences.

6. Find the average rate of change for the investor's plan and the 5-year CD between years 2 and 3, and between years 3 and 5. Explain what this shows in complete sentences.

7. One of your friends suggests another 5-year option that gives interest based on the function k(x) = 5000(1.02)x. Explain what the 1.02 represents in terms of the CD and if it is a better plan than the 5-year CD you found. Use complete sentences.

8. Make a final recommendation on what plan you and your friends should follow. Consider that you cannot collect your money from a CD until it has fully matured. Your recommendation should be at least three sentences long.

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