problem solving: find contradictory statements in model

K

kenkarylle5

New member
Joined
Mar 3, 2009
Messages
6
the united nations' department of economic and social affairs stated in 1999 that "the world's population stands at 6 billion and is growing at 1.3% per year, for an annual net addition of 78 million people.

A) this statement actually contains two contradictory descriptions of predicting world population growth. explain this contradiction.

B) using the information in the statement, construct a linear model for world population in billion in terms of years 1999. define variables

C) using the information in the statement, construct a exponential model for world population in billion in terms of years 1999. define variables

this is my intermediate algebra class..

please i need ur help tnxxx...
 
Let's look at some numbers (in billions) that show what the population is after 1999, using the statement that the population increases by 1.3% per year.

1999, 6.000
2000, 6.078 <-- I multipled 6 by 1.013
2001, 6.157 <-- I multiplied 6.078 by 1.013
2002, 6.237 <-- I multiplied 6.157 by 1.013
2003, 6.318 <-- I multiplied 6.237 by 1.013
2004, 6.400 <-- etc ...
2005, 6.483
2006, 6.568
2007, 6.653
2008, 6.740

In addition to stating that the population grows by 1.3% per year, they also stated that the ANNUAL increase is 78 million.

The word "annual" means that each year the population increases by 78 million. (78 million is 0.078 billion.)

Now let's look at some numbers (in billions) that show what the population is after 1999, using the statement that the population increases by 0.078 billion each year.

1999, 6.000
2000, 6.078 <-- I added 6.000 + 0.078
2001, 6.156 <-- I added 6.078 + 0.078
2002, 6.234 <-- I added 6.156 + 0.078
2003, 6.312 <-- I added 6.234 + 0.078
2004, 6.390 <-- etc ...
2005, 6.468
2006, 6.546
2007, 6.624
2008, 6.702

Is the contradiction clear, now? Can you explain it using complete sentences?



 
Re: problem solving due tomorrow need really help

yea i got it but the formula you used?

can you show me the model...

sorry i really suck on math, but i really tried my hard tho..
 
I can show you an example of a linear model, and then you can try to do the same with your exercise.

In 1999, I deposited $6,000 into a savings account that pays 10% SIMPLE interest, annually.

(If only!)

Simple interest is when the interest itself does not earn interest. In other words, after one year, the bank will deposit the $600 that the $6,000 deposit earned during the year (the balance will then be $6,600), but only the original $6,000 continues to earn interest. The $600 annual interest deposits never earn any interest themselves.

(When interest is paid on interest, then it's called "compounded interest".)

Since 10% of $6,000 is $600, the savings account balance grows by $600 each year.

This growth is linear because the growth rate never changes; it's always $600 per year. Therefore, the account balance can be modeled using a linear equation.

First, we define variables:

Let t = the number of years elapsed since 1999

Let y = the account balance

Here's the equation of the line:

y = 600 t + 6000

Are you familiar with the Slope-Intercept form of a linear equation? That's the form that this equation is in.

The slope is 600; the y-intercept is 6000.

How much money will be in the account in 2004?

2004 - 1999 = 5

Since five years elapse from 1999 to 2004, the value of t that we need is 5.

y = 600(5) + 6000

y = 3000 + 6000

y = 9000

There will be $9,000 after five years (2004).

1999, 6000 (t = 0)
2000, 6600 (t = 1)
2001, 7200 (t = 2)
2002, 7800 (t = 3)
2003, 8400 (t = 4)
2004, 9000 (t = 5)

Does this sort of reasoning and modeling ring any bells with what you've already been taught about linear equations and models?

The model in part (B) of your exercise will work in much the same way.

I'm guessing that when you typed "construct a linear model for world population in billion in terms of years 1999", you meant to say, "construct a linear model for world population (in billions) in terms of the number of years elapsed since 1999".
 
Re: problem solving due tomorrow need really help

ah ok..

i guess i kinda getting it now...
but still ima work on it..

thankyou so muchh appreciate it.
 
You must log in or register to reply here.
Top