Question

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

Answer 1

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

Answer 2

im on this question

Answer 3

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

Answer 4

HI!!

Answer 5

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

Answer 6

i dont understand the problem the equation

Answer 7

you can do it without using \[A=Pe^{kt}\] if you like

Answer 8

Hello @misty1212

Answer 9

i dont know how to use that either lol

Answer 10

lets make it easier and call 1992 year zero

Answer 11

the beginning population is 222 that is your \(P\)

Answer 12

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

Answer 13

ok lol

Answer 14

\[P=1222e^{kt}\] but you don't know \(k\) that is what you have to find

Answer 15

typo but whatever

Answer 16

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

Answer 17

so divide?

Answer 18

yeah divide
take the log
divide by 9

Answer 19

each sides by 9?

Answer 20

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

Answer 21

Please make sure to take the log before dividing by 9

Answer 22

i dont know the log

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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?

Answer 33

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

Answer 34

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

Answer 35

@ix.ty Hello?

Answer 36

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.