Question

I need some help please! :) I'm trying to figure out how to write an equation for population growth. It is estimated at 72 years to double at 1.1% and states that it needs to be dived but I don't understand how I would write it out. PLEASE HELP thank you :)

Answer 1

So the doubling time is 72 years? What's the 1.1% about?

Answer 2

that is what the rate is in growing

Answer 3

I need to figure out how to write the equation for it

Answer 4

If the population will double in 72 years you can calculate a rate.
If the rate is 1.1% per year, you can calculate the time to double.
I'd have to check to see if these are equal.

Answer 5

Well, close enough. Do you know the equation to use here?

Answer 6

let me get it

Answer 7

\[N = N_o e^{kt}\]

Answer 8

D = 72 and P=1.1

then D/P = about 65 years

(D = doubling time) and (P = annual percentage growth rate).
this is what the site says

Answer 9

That's not how it works.

Answer 10

Have you worked with exponential equations before?

Answer 11

I am trying those now I'm in algebra now and don't know how to do them lol

Answer 12

Well, you know about exponents right?

Answer 13

yes a little

Answer 14

Do you know what e is?

Answer 15

no

Answer 16

Where did you get this question?

Answer 17

I can explain the formula, but it may be a little hard for you. Want to try?

Answer 18

from a web site

Answer 19

yes I would love to try it

Answer 20

Great! The equation was
\[N = N_o e^{kt}\]

Answer 21

What that says is that the population as some future time t is equal to the current population No, times this factor which is e^kt. I'll explain the factor in the next post.

Answer 22

e is just this number, but the rate constant k is the 1.1% you gave, except you write it as 0.011. So if we have a population of 1000 today, and k = 0.011 then to calculate N you just do
\[N = 1000 e^{0.011 t}\]

Answer 23

Why don't we try 72 (years) for t? Do you have a calculator?

Answer 24

yes

Answer 25

I'm not exactly sure how you do this part, but basically you want to multiply 72 times 0.011 and then raise e to that power. Try doing the multiplication and then pushing "exp"

Answer 26

I get the value 2.2 from my computer.

>>> e**(72*0.011)
2.2078076288406323

Answer 27

72*0.011=0.792
is what I got

Answer 28

So with 0.792 entered press "exp"

Answer 29

I did not hit the exp
ok

Answer 30

I'm noot getting 2.2

Answer 31

even when I hit the exp

Answer 32

Well, you'll have to play with your calculator but 2.21 .. is the correct answer to this part. I'll explain what it means.

Answer 33

It means that the original 1000 will become 2200 after 72 years when growing with rate k = 0.011.

Answer 34

ok I will play with it some more

Answer 35

One last thing, there is a trick. The rate k times the doubling time T = ln(2) = 0.693. So you can go quickly from doubling time to rate, or back again just doing that multiplication.

Answer 36

ok so let me see if I got this

Answer 37

the time is 0.693^2

Answer 38

rate times the doubling time

Answer 39

the K is the 1000 or the 2200?

Answer 40

The k is 0.011

Answer 41

and those are the doubling

Answer 42

That's from your 1.1%

Answer 43

Go back to the equation. I give you a rate k = 1.1% = 0.01
I give you a time t = 72 years
I give you a population size = No
do No e^kt
That's the population at time t

Answer 44

I have the population

Answer 45

314,098,272

Answer 46

So that's the U.S. or something?

Answer 47

It states it takes 72 years to double that
let me get the whole statement

Answer 48

yes

Answer 49

To find the doubling time of a population at any given annual rate of growth, divide 72 by the annual percentage growth rate (in this case 1.1%). Current trends are as follows:

D = 72 and P=1.1

then D/P = about 65 years

(D = doubling time) and (P = annual percentage growth rate).

Because of our high rate of growth, the U.S. is one of the fastest growing countries in the industrialized word - we have grown from 150 million in 1950 to 275 million in 2000. It took all of human history for world population to reach 2.5 billion in 1950. Then, doubling just once during the next forty years, world population increased by 2.5 billion (a number equivalent to all preceding growth). U.S. population added 100 million people between 1950 and 1990, and if current rates of growth continue, will double in size to 550 million in the next 65 years. Examination of these numbers provides some understanding of the explosive nature of exponential growth; unfettered population growth is something the U.S. can ill-afford.

Answer 50

Just multiply 314,098,272 times the result we had before, 2.21

Answer 51

Wait, I have to explain someething.

Answer 52

694157181.1 is what I got

Answer 53

ok

Answer 54

What I gave you is the sophisticated answer, the one for true exponential growth (they mention that phrase toward the end). But because the problem is a bit complicated, as you saw, they have cheated a bit in the setup.

Answer 55

It's like the bank crediting your interest once a month instead of "instantaneously"

Answer 56

oh boy

Answer 57

So reading the question, I don't see a question there. They've given the answer.

Answer 58

see this is what confuses me I don't really know how to write them out that is why I came here

Answer 59

Maybe they want you to say, gee what if the rate was larger, like 2% annual growth. Then what would the doubling time be?

Answer 60

my answer don't meet theres

Answer 61

You have choices?

Answer 62

D=Doubling R=Rate
D= 72
Rate= 1.1%

Answer 63

that was as far as I got

Answer 64

I read what you posted and I don't see a question there. Sorry.

Answer 65

I basically need help with the equation
how to write it with the right answer lol