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# 4.07 4.07 Exploring Linear and Exponential Growth:

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## Mckenna Benjamin

on 16 July 2014

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#### Transcript of 4.07 4.07 Exploring Linear and Exponential Growth:

1. 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.
2-year CD...
Company's name: GE Capital Bank, interest rate (APY): 1.20%, minimum investment: \$500

5-year CD:
Company's name: Citizens Savings Bank and Trust Company, interest rate (APY): 1.21%, minimum investment: \$500

2. 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.
My function for the 2-year CD: f(x) = 500(1.20)^x
My work: 500(1.20)^2
=500(1.44)
F(x) = 720
My function for the 5-year CD: f(x) = 500(1.21)^x
My work: f(x) = 500(1.21)^5
=500(2.59374246)
f(x) = 1296.87123

3. 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.
f(x) = 5000+50x
x is the number of years.
4. Create a table showing the value of the two CDs and the investor's plan for 5 years.
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.
1.02 represents the interest rate of the 5-year CD that "one of my friends" is suggesting. The interest rate 1.02 means 2%. This plan is most likely better than my 5-year CD function because this interest rate is a greater percentage.
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.
The plan that I recommend we use is the 5-year plan that my "friend" came up with. If we were to use my interest rate (plan), than by the time the CD matures, we will have less money, than if we were to follow "my friends" plan. Our best choice is to follow her 5-year CD plan and my 2-year CD plan.
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.
To prove the the investor's plan is a linear function, you must look at the graph and figure out its pattern. You need to see if the numbers increase each year by the same rate. So, yes the investor's plan is a linear funtion because it increases by \$50 each year.
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.
The average rate of change for the investor's plan is \$50 each year. The 5-year CD between 2 and 3 is 1.21 and as for years 3 and 5, it is the same, 1.21. This shows that the average rate of change of the investor's plan and the average rate of change of the 5-year CD, between years 2 and 3, and between years 3 and 5 are linear functions.
GOAL!
4.07 Exploring Linear and Exponential Growth:
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.

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.
2 year CD
5-year CD
Investor
Year 1
Year 2
Year 3
Year 4
Year 5
720
864
1036.8
1244.16
1492.992
1296.87
1569.2127
1898.74
2297.48
2779.95
5050
5100
5150
5200
5250
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