Gabriel Hernández 4.07: Exploring Linear and Exponential Growth July 10, 2014

1. Company name: American Express

APY: 2− year 0.70% 5− year 1.35%

Maximum deposit: $0.00Compound daily

2. The general function is

f ( x )=P ¿Where P is the principal, r is the APY, x is the number at years.

P=5,000 P=5,0002-years 5-years

r=0.70% r=1.35%

f ( x )=5,000¿ g ( x )=5,000¿

f ( x )=5,000¿ g ( x )=5,000 (1.0135 )x

3. h ( x )=5,000+50 x

4.

Year 1 Year 2 Year 3 Year 4 Year 52-year CD 5,035 5,070.25 5,105.74 5 ,141.48 5,177.475-year CD 5,067.50 5,135.91 5,205.25 5,275.52 5,346.74Investor 5,050 5,100 5,150 5,200 5,250

5. The investor’s plan is a linear function because it increases by the same amount each year, and the CDs are exponential functions because the variable that represents time in each CD function is an exponent.

6.5 year from a=2 to b=3

g (3 )−g(2)3−2

=5,205.25−5,135.91

3−2=66.34

Investor from a=2 to b=3h (3 )−h (2)3−2

=5,150−5,100

3−2=501

=50

5-year from a=3 to b=5

Gabriel Hernández 4.07: Exploring Linear and Exponential Growth July 10, 2014

g (5 )−g(3)5−3

=5,346.74−5,205.25

5−3=70.725

Investor from a=3 to b=5h (5 )−h (3)5−3

=5,250−5,150

5−3=1002

=50

The average rate of change for the 5-year CD and Investor’s Plan from year 2 to year 3 shows how much money per year the two plans would be earning from year 2 to year 3. The average rate of change for the 5-year CD and Investor’s Plan from year 3 to year 5 shows how much money per year the two plans would be earning from year 3 to year 5.

7. The APY for this CD is 2%. This is a better plan than the 5-year American Express CD because each year a lager percent of the principal is used to calculate the interest.

8. If we need the money back right away because we have a new business, I would recommend the American Express 2-year CD because it will give us the most money in the shortest amount of time. If we were looking for the most amount of money to be made, I definitely would not go with the investor’s plan because linear functions don’t increase quickly over time. I would go with the 5-year CD from American Express since it will have earned the most money after 5 years (I would pick my friend’s suggestion k(x), but I’m not sure if I’m allowed to do that).