Question

in 1987, the world population was 5 billion. before 1987, the growth rate was about 1.6% each year. predict the world population in 2027 if the grwoth rate in 1987 and subsequent years
i) continues to be 1.6% each yr
ii) changes to 3.5% each year
iii) decreases to 1.1% each year

Answer 1

Here's a formula::

\[ \Large \textrm{initial_population} \cdot (100\% + 1.6\%)^\textrm{years} = \textrm{final_population} \]

Answer 2

Lemme write that again:

final_population = initial_population * (100% + growth_rate)^years

Answer 3

This is also called Exponential Growth.

http://en.wikipedia.org/wiki/Exponential_growth

Answer 4

alright so for the first eqn it would be
\[final population = 5\times10 ^9 ( 1+0.016)^{40}\]

40 yrs since thats the amount of yrs in between 2027 and 1987

Answer 5

@muntoo you there? :S

Answer 6

Yep. :)

If you're confused whether it's 40 or 41 years, just remember: you're not including the first year, so 2027-1987 works.

If you're not confused... just ignore what I said.

Answer 7

thank you !
also, it asks me to graph it... but when i do ... i just get a line.... /:
im not so sure how to do this part

Answer 8

@muntoo

Answer 9

the first one, i got 9,434,490,000, and when i graphed it, i get just a horizontal line /:

Answer 10

It should look something like this:

http://www.wolframalpha.com/input/?i=y+%3D+5+*+10%5E9+%281%2B0.016%29%5Ex%2C+x+from+0+to+40

Notice how it curves just a tiny bit. Again, this is called exponential growth.

When you have:
\[\large y = (1+r)^t, \textrm{ where } r \textrm{ is the growth rate, and } t \textrm{ is time}\](Notice that you can use 'x' instead of 't'.)

The r determines how curved the graph is. If you have a positive value, it will have an upwards curve like these (excluding the y=1 graph, which doesn't have any curve):

http://www.wolframalpha.com/input/?i=y%3D1%2C+y%3D1.25%5Ex%2C+y%3D1.5%5Ex%2C+y%3D2%5Ex%2C+y%3D2.5%5Ex%2C+y%3D3%5Ex

The greater the value of r, the more curved it will be.

To plot yours, just plot both points and draw a slight curve to connect them. Since r=0.06, it's not going to have much of a noticeable curve.

Answer 11

Graphing these with just two points is complicated, so I would figure out an 'intermediate' point in the middle if I were you. Set x=20 and determine your y value. Then, you can confidently draw a line the points knowing the graph looks something like that.

Answer 12

oh okay thank you @muntoo :)

Answer 13

You're welcome. :)