Solve Math Problem: When Will PEI Population Surpass Newfoundland?

  • Thread starter joejo
  • Start date
In summary: I can't remember precisely. But we certainly did logs at 14 (grade 10).In summary, the conversation discusses the population of Newfoundland and Labrador in 2001, with Newfoundland experiencing a decrease and PEI experiencing an increase. The conversation then delves into finding the year in which the population of PEI will surpass Newfoundland's, using various equations and methods. The final answer is found to be 2170, with the population of PEI starting to overtake Newfoundland's. The conversation also touches on the topic of logarithms, with some participants mentioning they were introduced to them in grade 11 math, while others were introduced earlier.
  • #1
joejo
150
0
Hi guys...can someone help me out with this problem...

The population of Newfoundland and Labrador was 533,800 in 2001. At that time the population of Newfoundland was decreasing at a rate of 0.6% per year. The population of PEI was 138,500 in 2001. At that time the population was increasing at a rate of 0.2% per year. In what year will the population of PEI be more than Newfoundland? Explain?


I have this so far: y=#of years

533,800(1-0.006)^y

138,500(1-0.002)^y


Now what?
 
Physics news on Phys.org
  • #2
the equation of pop. growth is y(t) = y0 * e ^(kt)

where y0 is beginning pop
k is the growth rate
and t is the time

plug in the values and make them equal to each other and solve for t
 
  • #3
we haven't done that yet..any other way...
 
  • #4
138,500*(1+0.002)^y = 533,800*(1-0.006)^y
138,500*(1.002)^y = 533,800*(0.994)^y
ln(138,500*(1.002)^y) = ln(533,800*(0.994)^y)
ln(138,500) + ln((1.002)^y) = ln(533,800) + ln((0.994)^y)
ln(138,500) + y*ln(1.002) = ln(533,800) + y*ln(0.994)
y*ln(1.002) - y*ln(0.994) = ln(533,800) - ln(138,500)
y = ln(533,800/138,500) / ln(1.002/0.994) = 168.3

2001 + 168.3 = 2169.3

... theoretical
 
  • #5
Thx faruk but wats ln?
 
  • #6
Natural log
 
  • #7
i haven't done logs yet...this is suppose to be grade 11 math...
 
Last edited:
  • #8
It's been many years since I've done stuff like this but isn't it the same sort of calculation as working out compound interests?

Create a graph with the decreasing population of Newfoundland represented using one colour and then do the same for Labrador. Where the line cross is where they equal each other.
 
  • #9
joejo said:
i haven't done logs yet...this is suppose to be grade 11 math...

*joejo, logarithms are used to find exponents, which would be the years in your problem. For example, solving for [itex] c [/itex] in the equation
[tex] a = b^c ,\left( {a,b,c} \right) \in \mathbb{R} [/tex]
will give you
[tex] c = \log _b a \Leftrightarrow \frac{{\log a}}{{\log b}} \Leftrightarrow \frac{{\ln a}}{{\ln b}} [/tex]
*What's left is just plugging in values (*hint:smile:*)
---------------------------------------------------------------------
*P.S., I am a high school junior too (Grade 11), and the mathematics
at my school can seem at times quite slow as well :shy:;
[tex] \downarrow [/tex] For example, I just finished second-semester calculus this year, but I
could have studied it as a sophomore last year (i.e., in 10th grade :rolleyes:~)
 
Last edited:
  • #10
11th grade: that's 16yrs old? Is that the equivalent of O levels (GCSE's)
 
  • #11
Daminc said:
Is that the equivalent of O levels (GCSE's)

No-one calls them O Levels any more :smile:. Edit: A Levels still remain A Levels, though!
 
  • #12
You can also do it by the trial and error method

For Newfoundland : 533800*(1-0.006)^t => 533800*(0.994)^t
For PEI: 138500*(1+0.002)^t => 138500*(1.002)^t

Start with t+0 (t equals the number of years elapsed) and start jumping:

when t=20 Newfoundland=476123.8 & PEI=143858.8 which is no good

t=120 gives Newfoundland=259265.5 & PEI=176025.8 which is closer

t=150 gives Newfoundland=216439.4 & PEI=186899.4 which is closer still

t=170 gives Newfoundland=191895.1 & PEI=194519.2 has overshot a little

t=168 gives Newfoundland=194218.7 & PEI=193743.4 nearly there

t=169 gives Newfoundland=193053.4 & PEI=194130.9 which is the number you want

2001+169=2170 which is the year PEI overtakes Newfoundland :)
 
  • #13
No-one calls them O Levels any more

Hah, I'm old. Leave me alone :cry:

t=169 gives Newfoundland=193053.4 & PEI=194130.9 which is the number you want

2001+169=2170 which is the year PEI overtakes Newfoundland :)

Mmmm, the crossover occurs in the later part of 168 so the year would be 2169 (I think)
 
Last edited:
  • #14
joejo said:
i haven't done logs yet...this is suppose to be grade 11 math...
I would think they would have at least introduced common logs (base 10). Or maybe I'm old, too. When I was in high school, you had to have some understanding of logs or you wouldn't understand your calculator. But then, our calculators were three pieces of bamboo lashed together.
 
  • #15
Actually, in Belgium logs are introduced in grade 12, but that may not be a great reference... :rolleyes:
 
  • #16
thanks guys...you all helped out a bit...Damincs answer was the way we did it in the book...Thanks Daminc!
 
  • #17
This is what I have JoeJo:

Consider differential equations for both places:

[tex]\frac{dN}{dt}=-0.006N[/tex]

[tex]\frac{dP}{dt}=0.002P[/tex]

Solving them with the initial conditions given and equating them for when the populations just become equal we get:

[tex]533800e^{-0.006t}=138500e^{-0.002t}[/tex]

little of this, little of that, we get t=169 so in 2170 the populations become equal as PEI starts to overtake the other one.

Edit: I'm such a slow-poke. :yuck:
 
Last edited:
  • #18
I would think they would have at least introduced common logs (base 10). Or maybe I'm old, too. When I was in high school, you had to have some understanding of logs or you wouldn't understand your calculator.
When I was younger I think we were introduced to logs by having a small blue book filled with numbers. Can anyone else remember that book?

p.s. I'm sure we did logs when we were about 12-13 or so.
 

1. How is the population growth of PEI and Newfoundland currently trending?

The population of PEI has been steadily increasing over the years, with a growth rate of 1.05% in 2020. Newfoundland, on the other hand, has experienced a decline in population with a growth rate of -0.3% in 2020.

2. What is the current population of PEI and Newfoundland?

As of 2020, the population of PEI is approximately 159,625 and the population of Newfoundland is approximately 520,437.

3. Based on current trends, when is the projected date for PEI's population to surpass Newfoundland's?

According to population projections, PEI's population is expected to surpass Newfoundland's in the year 2027.

4. What factors contribute to the difference in population growth between PEI and Newfoundland?

One of the main factors contributing to the difference in population growth between PEI and Newfoundland is the difference in economic opportunities and job prospects. PEI has experienced a growth in industries such as tourism and agriculture, while Newfoundland's economy has been heavily reliant on the declining fishing industry. Additionally, PEI has a higher immigration rate compared to Newfoundland, which also contributes to its population growth.

5. Will the projected date for PEI's population surpassing Newfoundland change in the future?

The projected date for PEI's population surpassing Newfoundland may change in the future depending on various factors such as economic growth, immigration rates, and potential changes in government policies. However, based on current trends, it is expected that PEI's population will surpass Newfoundland's in the near future.

Similar threads

  • General Math
Replies
1
Views
982
  • General Math
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
12
Views
2K
  • Calculus and Beyond Homework Help
Replies
13
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Differential Equations
Replies
1
Views
6K
Replies
11
Views
3K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
2K
Back
Top