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## anonymous one year ago will give a medal! A country's population in 1992 was 222 million. In 2001 it was 224 million. Estimate the population in 2004 using the exponential growth formula. Round your answer to the nearest million. P = Aekt

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1. anonymous

What about the last question??? The way to solve this problem is nearly exactly the same as the last one.

2. anonymous

im on this question

3. anonymous

Help me help you, do you understand what that formula represents, what the goal is of the problem, etc etc. Please tell me what you know and I will tailor my approach to that

4. misty1212

HI!!

5. anonymous

I understand, but if you don't understand the last problem the solutions for the two are almost exactley the same.

6. anonymous

i dont understand the problem the equation

7. misty1212

you can do it without using $A=Pe^{kt}$ if you like

8. anonymous

Hello @misty1212

9. anonymous

i dont know how to use that either lol

10. misty1212

lets make it easier and call 1992 year zero

11. misty1212

the beginning population is 222 that is your $$P$$

12. misty1212

lol no, not the way they asked the question, that is your A

13. anonymous

ok lol

14. misty1212

$P=1222e^{kt}$ but you don't know $$k$$ that is what you have to find

15. misty1212

typo but whatever

16. misty1212

then since 9 years later it is 224 you can solve $\large224=222e^{9k}$ for $$k$$

17. anonymous

so divide?

18. misty1212

yeah divide take the log divide by 9

19. anonymous

each sides by 9?

20. anonymous

@ix.ty Do you see why you need to take the log?

21. anonymous

Please make sure to take the log before dividing by 9

22. anonymous

i dont know the log

23. misty1212

$224=222e^{9k}\\ \frac{112}{111}=e^{9k}\\ \ln(1.009)=9k\\ k=\frac{\ln(1.09)}{9}$

24. misty1212

oh, if you don't know about logs you can's use this method

25. anonymous

@misty1212 this is the same issue that cam up on the previous problem I was working with @ix.ty

26. anonymous

Ok as I discussed before the natural logarithm is the INVERSE function of the exponential function.

27. anonymous

@ix.ty Do you know what an inverse function means? If so, could you tell me and perhaps give an example please.

28. anonymous

it reverses another funtion f(x)=-1/3x+1 youll but a y infront of the "fx"

29. anonymous

Exactley, an inverse function reverses the action of a function. But to make it a little more rigorous, given an equation of the form y=f(x) where given an value x the function f gives me a value y that is related in a one-to-one fashion with x..... the inverse function (forgoing the discussion of domain and other issues) f^-1(y)=x is how given the y value I can find the corresponding x value that is related to it in a one-to-one fashion

30. anonymous

Ok so if f(x)=x^3 then in order to find the value y=x^3 I have to apply the inverse function which happens to be the cube root: i.e. (y)^(1/3)=(x^3)^(1/3)=x^(3/3)=x

31. anonymous

SO.... the exponential function that is at the cent of this who exponential growth and decay has an inverse function called the logarithm

32. anonymous

Now lets forgo for the moment the idea of e and the natural exponential and the natural logarithm and ask ourselves the question what does exponential growth and decay mean. You first, what does exponential growth mean, and can you give me an example please?

33. anonymous

Sorry the grammar/spelling is so poor, but typing in this text box causes it to bounce around for some reason and given I think faster than I type I sometimes gloss over letters and words sometimes..... what I meant to say above was the exponential function is at the center of of all these exponential growth and decay questions

34. anonymous

The reason why I am trying to go into detail is if you don't understand what it is and where it comes from, these problems will continually give you trouble

35. anonymous

@ix.ty Hello?

36. anonymous

Alright, well I tried twice now to help, but it is a two way street. If I can't get any reciprocity, then I can't help.

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