Question

help pweassssssssse

In 2010, the 2009 populations and projected population rates were released for Russia and Ethiopia. The population of Russia in 2009 was 140.9 million; the population of Ethiopia was 82.8 million. Russia is decreasing in population by approximately 0.4% annually; the population of Ethiopia is growing at 2.6%. Using logs and letting x be the number of years since 2009, answer the following questions.

Answer 1

a. How long, at the above rates, will it take for the population of Ethiopia to double?

b. How long, at the above rates, will it take for the population of Russia to reach 125 million?

Answer 2

we use the excel fo problems like this btw

Answer 3

for*

Answer 4

This is similar to our other question. For Ethiopia, you don't even need a number for the population though. Let initial population be P and eventual population be 2P.

Answer 5

I have to take off... good luck... glad to see you're in good hands with @tcarroll010

Answer 6

P(1.026)^x = 2P. Or, more simply, (1.026)^x = 2. Can you do logs now the way I showed you?

Answer 7

b is around 2038

Answer 8

what do u insert in replacement of x i dont understand that part

Answer 9

I didn't get to b yet, I'm still on a. You young folk are so fast! x(log(1.026)) = log(2).

Answer 10

x is the passage of years in number of years.

Answer 11

actually around 2039 would be more accurate for b but i have no clue how to use logs

Answer 12

a is definietly a problem for me

Answer 13

27.005 years for part a. Do you agree?

Answer 14

can u go thru the steps with me please? i hate to admit it but im a bit slow with the logs

Answer 15

absolutely no problem. A lot of math is letting things sink in. You're not expected to be an expert right off. But to learn, you will have to get the concepts down after reviewing the steps and answers which is what you should do when anyone helps you. Try to do the whole problem again yourself if you got lots of help.

Answer 16

For Ethiopia, we are being asked how long does it take for the population to double, so it doesn't really matter what the initial population is. The concept will work for whatever the initial population is.

Answer 17

yea

Answer 18

So, initial pop is P and eventual pop is 2P. This will simplify things. You could work with the actual numbers but that muddies up what is being asked. Clearer this way, you'll see.

Answer 19

82.8(1+.026) is this used at all

Answer 20

That's a good and commendable attempt and will lead to the right answer, but better and more mathematically elegant to say P(1.026) after the first year and P(1.026)^2 after the second and P(1.026)^x after the xth year.

Answer 21

oh ok

Answer 22

how would we apply this to the logs

Answer 23

You are then looking for P(1.026)^x >= 2P

Answer 24

2P because we're looking fo the doubled amount?

Answer 25

Here's where the elegance and clarity come into play. With P and 2P you are driving home the concept of doubling. Also >= because you want to "get to" 2P and the > in >= emphasizes that you are looking for a minimum value for x. Yes, 2P for doubled amount.

Answer 26

oh ok

Answer 27

And the beauty of P(1.026)^x >= 2P shows 2 things. 1) emphasizing doubling, and 2) that the initial value of P doesn't matter because of the obvious cancellation. So, you get (1.026)^x >= 2. Simpler is better.

Answer 28

kk

Answer 29

Since x is in the exponent, logs are needed to solve. So, taking logs of both sides, we get x(log(1.026)) = log(2).

Answer 30

Sorry, x(log(1.026)) >= log(2).

Answer 31

ok

Answer 32

im writing all this down

Answer 33

Easy solving logs and simple division gives 27.005 rounded.

Answer 34

Take your time. Of course, you always have access to this question since you own it and can get to it.

Answer 35

is there division involved?

Answer 36

That last equation, x(log(1.026)) >= log(2), becomes x >= log(2) / log(1.026). That's the division.

Answer 37

With a numerical answer of 27.005, you can how ridiculous it would be to multiply (1.026) by itself 27+ times to get to 2. But, instead of multiplying 27+ times, you could just use your calculator to try (1.026)^27.005 to see how this works.

Answer 38

2

Answer 39

Yes, and nice that logs exists that allow us to work backward.

Answer 40

so it would only take 2 years to double their population?..

Answer 41

wait that doesnt sound likely

Answer 42

No, 27.005 to double. 2 is the "twice"

Answer 43

ohhhhhh oh ok i see

Answer 44

P(1.026)^27.005 = 2P. x is the years and is 27.005

Answer 45

yes i see now

Answer 46

Don't worry, you'll get it. It does take some time. Logs and exponents is where I see a lot of people get confused at the start. But just stick with it.

Answer 47

so did i do b correctly?

Answer 48

You appeared to get an answer of about 29 years for b? Is that right? I didn't do b yet, but I could do it and check.

Answer 49

yes can u check for me i got the year 2039

Answer 50

am i supposed to use logs for this cuz i didnt i used a simpler method

Answer 51

140.9(0.996)^x <= 125 is the formula

Answer 52

Well, whatever is easiest for you. I use logs because that is what is easiest for me.

Answer 53

yes thats what i used lol i guess i was right afterall then

Answer 54

logs r so difficult for me i need alot more practice

Answer 55

x(log(0.996) <= log(0.88715)

Answer 56

then u divide that?

Answer 57

x is 29.874

Answer 58

Yes. How did you do this without logs?

Answer 59

wait ... i think i did it wrong then

Answer 60

i did 140.9(1-.004)

Answer 61

Well, you're very close and since you approximated, I'd say you got an ok answer with year 2039 because that is about 30 years from 2009. (1 - 0.004) is the same as my 0.996 so you are ok with that.

Answer 62

Didn't you use (1 - 0.004)^x somewhere?

Answer 63

x(log(0.996) <= log(0.88715)

Answer 64

do u divide that

Answer 65

Yes, like the part a. you divide out the log expression on the left to isolate x.

Answer 66

so log0.996/log0.88715= 29.874?

Answer 67

Just one change in my equation. I should have put >= not <=. As for your question, switch the numerator and denominator.

Answer 68

so log0.88715/log0.996= 29.874?

Answer 69

So, with that, you're done!

Answer 70

hmmm still need practice but thank u so much

Answer 71

You'll get it. Just practice and review.

Answer 72

kk thank u

Answer 73

you're welcome