anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
What about the last question??? The way to solve this problem is nearly exactly the same as the last one.
anonymous
  • anonymous
im on this question
anonymous
  • 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

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misty1212
  • misty1212
HI!!
anonymous
  • anonymous
I understand, but if you don't understand the last problem the solutions for the two are almost exactley the same.
anonymous
  • anonymous
i dont understand the problem the equation
misty1212
  • misty1212
you can do it without using \[A=Pe^{kt}\] if you like
anonymous
  • anonymous
Hello @misty1212
anonymous
  • anonymous
i dont know how to use that either lol
misty1212
  • misty1212
lets make it easier and call 1992 year zero
misty1212
  • misty1212
the beginning population is 222 that is your \(P\)
misty1212
  • misty1212
lol no, not the way they asked the question, that is your A
anonymous
  • anonymous
ok lol
misty1212
  • misty1212
\[P=1222e^{kt}\] but you don't know \(k\) that is what you have to find
misty1212
  • misty1212
typo but whatever
misty1212
  • misty1212
then since 9 years later it is 224 you can solve \[\large224=222e^{9k}\] for \(k\)
anonymous
  • anonymous
so divide?
misty1212
  • misty1212
yeah divide take the log divide by 9
anonymous
  • anonymous
each sides by 9?
anonymous
  • anonymous
@ix.ty Do you see why you need to take the log?
anonymous
  • anonymous
Please make sure to take the log before dividing by 9
anonymous
  • anonymous
i dont know the log
misty1212
  • misty1212
\[224=222e^{9k}\\ \frac{112}{111}=e^{9k}\\ \ln(1.009)=9k\\ k=\frac{\ln(1.09)}{9}\]
misty1212
  • misty1212
oh, if you don't know about logs you can's use this method
anonymous
  • anonymous
@misty1212 this is the same issue that cam up on the previous problem I was working with @ix.ty
anonymous
  • anonymous
Ok as I discussed before the natural logarithm is the INVERSE function of the exponential function.
anonymous
  • anonymous
@ix.ty Do you know what an inverse function means? If so, could you tell me and perhaps give an example please.
anonymous
  • anonymous
it reverses another funtion f(x)=-1/3x+1 youll but a y infront of the "fx"
anonymous
  • 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
anonymous
  • 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
anonymous
  • anonymous
SO.... the exponential function that is at the cent of this who exponential growth and decay has an inverse function called the logarithm
anonymous
  • 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?
anonymous
  • 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
anonymous
  • 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
anonymous
  • anonymous
@ix.ty Hello?
anonymous
  • 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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