## perl 2 years ago Oil consumption is increasing at a rate of 1.9% per year. What is its doubling time? I'm not sure if this is linear increase or exponential. if its linear

1. perl

, no , this website says its exponential http://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.112025.html

2. perl

, if its linear then y = Ao ( 1 + .06*t ) if its exponential then y = Ao ( 1 + .06)^t

3. uzumakhi

i think its exponential 2 = 1 ( 1 + 0.06)^t now calculate t

Oh, wait. That's right. I apologize. I graphed it wrong.

5. perl

how will i know if its exponential or not?

6. perl

here is another example http://www.physics.uoguelph.ca/tutorials/exp/intro.html

7. perl

why isnt the following example linear ? "For example, let's look at a population of wee beasties which increases by 10% per year. If there were 100 wee beasties now, there would be an increase of 10 wee beasties after a year. "

8. uzumakhi

see in question it increases 1.9% per year first year let consumption = x next year = 1.9*x/100 later year = 1.9(1.9*x/100)/100 if you plot its graph you get exponential curve try it

9. uzumakhi

in your second example population first year = 100 population second year = 110 population third year = 121 it also not linear

10. perl

you need a plus somewhere

11. perl

it should be next year consumption = last year consumption* ( 1 + 1.9/100)

12. uzumakhi

yes you are write

13. perl

so we have x1 = x x2 = x1 (1.019) x3 = x2 (1.019) = [x1 (1.019) (1.019) ]

14. perl

better start with zero, x0 = x x1 = x0 (1.019) x2 = x1 (1.019) = [x0 (1.019) ] (1.019) = x0 (1.019) ^2

15. uzumakhi

calculate x1,x2 ,x3 and try to find x2 - x1 = x3 -x2 if its write then only its linear

16. perl

so did you agree with my math?

17. perl

right, clearly x2-x1 != x3 - x2

18. uzumakhi

yes i agree so what you think its linear or exponential

19. perl

well... exponential

20. perl

i think its a little ambiguous however

21. perl

, you could also have y = x0 ( 1 + .019 * t ) , no ?

22. perl

ok how would you word it so that it is linear?

23. uzumakhi

let if increase every year is same then its linear for example if population of city inc by 20 people every year then we can say that its linear

24. perl

ok , so we wouldnt use percentage for a linear increase

25. uzumakhi

yes

26. perl

if there is a percentage growth , like population percentage growth , grows at a constant percentage, it is exponential growth

27. uzumakhi

yes

28. perl

got it,

29. uzumakhi

ok then

30. perl

ok now doubling time makes sense

31. perl

doubling time is the time it takes for the initial amount to grow 100% , leaving you with double

32. uzumakhi

33. perl

yes, the math i didnt have trouble with. just the understanding

34. perl

i have a much harder problem, differential equation

35. perl

36. perl

its a logistic growth problem

37. uzumakhi

ok then now you can close the qustion after giving me medal...............lol

38. perl

you stuck it out , good work

39. perl

the rest bailed