Question

A country's population in 1990 was 123 million.In 2002 it was 128 million.Estimate the population in 2013 using the exponential growth formula.(P=Ae^kt).Round to the nearest millionth..

Answer 1

@Hero

Answer 2

@GoldPhenoix

Answer 3

@science0229

Answer 4

P=Number of Population..
A=Number Of Population At Time..Which Is 0?
K=Positive Constant..
E=The Natural Logarithm Base?

Answer 5

Thats What I Have In My Notes.

Answer 6

How about t?

Answer 7

t=0

Answer 8

t can't be zero, and neither can be A.

Answer 9

This is what I think.
I think t is the year, and A and k are positive constants, which we have to solve for.

Answer 10

Sorry For The Misunderstanding..A=Number Of Population A Time..Time,AKA T=0

Answer 11

At The Time*

Answer 12

What do you mean?

Answer 13

Do It Your Way,Im Very Unsuccessful I These Types Of Problems..

Answer 14

ok

Answer 15

So, you're given 2 positive variables and 2 data points.

Answer 16

Wait, sorry.
2 equations.

Answer 17

Yes.

Answer 18

You're given 2 data points to solve for 2 variables, 'A' and 'k'.
First equation is \[123=Ae ^{1990k}\] (I'll skip writing million for 123)
Second equation is \[128=Ae ^{2002k}\].
If you divide second equation by first equation, you'll get\[\frac{ 128 }{ 123 }=e ^{12k}\].

Answer 19

By the definition of ln, \[12k=\ln \frac{ 128 }{ 123 }\]

Answer 20

Alright.. So With e^12k,You Plug In e and k?

Answer 21

Divide both sides by 12, and you'll get \[k=\frac{ 1 }{ 12 }e ^{12}\].
That's k.

Answer 22

Okay.

Answer 23

Now, you can plug that in for either of the equation, and find A using a calculator.

Answer 24

After you find A and k, you get a complete function that tells you the population in millions for a certain year, t.

Answer 25

So you plug in 2013 and round to the nearest millions.

Answer 26

My Calculator Doesn't Support Fractions With Exponents..

Answer 27

Then you can try going to one of the online calculators.

Answer 28

Okay

Answer 29

I Got 134.232323?

Answer 30

I Used This Calculator http://www.wolframalpha.com/

Answer 31

Just a second

Answer 32

Wait!!!

Answer 33

I'm really sorry.

Answer 34

k is supposed to be \[\frac{ 1 }{ 12 }\ln \frac{ 128 }{ 123 }\].

Answer 35

But that's basically how you do this problem.

Answer 36

Sorry, again.

Answer 37

So After I Round,I Got 133? Correct?

Answer 38

@science0229

Answer 39

if you got A and k correct, and you made no mistakes, that should be correct.

Answer 40

I'm not going to tell you the answer, but if you didn't make any calculation mistakes, that's the right answer.

Answer 41

It Was Wrong..But Thanks Anyways,It Really Helped When You Explained It.Thanks :)

Answer 42

Welcome :)