## Day_2010 2 years ago Can someone explain the exponential growth formula in layman's terms? I really need the help understanding the concept, any help will be greatly appreciated! :)

1. Sheng

ok say...i have some amount of money deposited in a bank collecting interest given time the amount will "exponentially increase" because interest is based on how much money i have since each year my money will increase, as time increases, interest exponentially increases. example 2. bacterial growth...say you start off with 1 colony of bacteria, given enough time/resources, it will exponentially grow

2. Day_2010

hmm that makes sense, but what I can't figure out is how to apply that to the formula A=A\[_{0}\]^rt

3. Day_2010

|dw:1352091524486:dw|

4. Day_2010

5. Sheng

Ao = initial amount, r = rate, t = time e = natural logarithm

6. Sheng

so say given a scenario...i have \$1000 deposited at a rate of 7% interest per year, how much will i have in 100 years

7. Day_2010

I had a problem understanding "after year 2003" or whatever year it may be in a "problem"... they say to input t=0 ..... why does t=zero?

8. Day_2010

9. Sheng

t = 0 for initial time im assuming

10. Day_2010

One sec.. I will write the problem for you to see..

11. Day_2010

The exponential model |dw:1352091910349:dw| describes the population, A, of a country in millions, t years after 2003. .... use the model to determine when the population of the country will be 771 million.

12. Sheng

is that an rt?

13. Day_2010

the 0.026 = r

14. Sheng

oh ok

15. Day_2010

lol sorry it's very sloppy

16. Sheng

t = 0 for 2003 because that is the initial population, the 642 million

17. Sheng

for any years after 2003, you would do say 2008, 2008-2003 = 5, to t = 5

18. Day_2010

OH hmm that makes plenty of sense... my professor does not do a good job at explaining things lol

19. Sheng

np hope it helped

20. Day_2010

so it's zero because it's the initial right? just making sure I understand lol

21. Sheng

it's zero because you are given the initial population at year 2003 remember Ao = 642 million, so if t is any value but 0 for 2003, you would get a different number for Ao, which wouldn't be the case :)

22. Day_2010

Okie dokie! Thanks... I really appreciate the help. :)

23. Day_2010

Your awesome.. I'm looking at my homework and now I understand it. lol

24. Sheng

sometimes just takes another perspective in things to understand :)