How do I know if its constant or exponential and how it changed?

Question

Time (year) Investment A (dollars) Investment B (dollars)

0 3500 4000

1 3800 4200

2 4000 4410

3 4300 4631

4 4500 4862

Angela followed two investment portfolios over five years.

Which statement best describes the results?

a. Both investments changed at constant rate.

b. Both investments changed exponentially.

c. Investment B changed at constant rate.

d. Investment B changed exponentially.

Answer 1

Constant growth means that it grew by the exact same amount every year.

Investment A grew by $300, $200, $300, $200. That is not constant growth.

Investment B grew by $200, $210, $221, $231. That is not constant growth.

For exponential growth to occur, it will increase by the same percentage each year.

To calculate percent growth, divide the new value by the old value. subtract 1, then multiply by 100 to get into percent growth form.

Investment A grew by 8.57%, 5.27%, 7.5%, 4.65%. That is not exponential growth.

Investment B grew by 5%, 5%, 5.01%, 4.99%. That is exponential growth (with some rounding errors, because you'll rarely end up with exact whole numbers in growth equations)

example of calculating percent growth:

4200/4000 = 1.05

1.05-1 = 0.05

0.05*100 = 5%

4410/4200 = 1.05

etc...

Hope this helps! let me know if you have any questions!