## November 09, 2006

### Scribe post

hello guys!!!!
In today's scribe we are going to talked about matters regarding our scribe post because earlier we had an issue about this. Then, on the latter part of my post, I'm going to show you the answers to our word problems. First of all, Mr. K gave us guidelines on how to post our scribes then he discussed to us the limitations regarding our posts.

I f you want to review the "student made this" you can

After that he also mentioned that we are not allowed to use items from the internet that are copyrighted, instead, use items with a label CC inside a circle or record your own music then download it in your blog so you will not be sued but again, these are just reminders that are better to be followed than to put yourself in trouble because our blog is part of our classroom activity and it is not just an ordinary website to visit. On the other hand, these are the answers to our yesterday's word problem.

1) The population of Toronto was 4,000,000 in 2000. It grows by 1.2% eah year. In what year will the population be 6,400,000?

Given:
A= 6.4 million
Ao= 4 million
m= 1.012
( "m" becomes 1.012 because we add the original rate of population, which is 100% and when converted to decimal will become 1. Then we add 1.2% to 1, which when converted to decimal will become 0.012. Therefore, the equation will become 1+0.012= 1.012. It is wrong to write 0.012 as the value of "m" because when we used it to find the population in the next year the result will be smaller. For example, if there are 100 people in 2000 then in 2001 the number of people will become 101.2 because we just add 1.2% as the rate in the population. As a result, the increase of people become less or decays. Instead, in this example, we should write 0.988 as the value of "m" because population increase or grows everytime. This number came by subtracting 1.2 from 100 resulting into 98.8 and when converted to decimal will become 0.988.)
t= ?
p= 1

Formula: A= Ao m^ (t/p)

Solution:
6.4= 4( 1.012) ^t

(6.4/4) = 1.012^ t

ln (6.4/4)= t ln (1.012)

[ ln(6.4/4)]/ (ln 1.012)= t

39.4015= t

Therefore, the population will be 6,400,000 in year 2039 because we add the answer with 2000 ( 2000+ 39= 2039).

2) You have \$10,000 and invest it all at 12% compounded quarterly. How long will take tou to be a millionaire?

Given:

A= 1,000,000
p= 10,000
r= .12
n= 4
t= ?

Formula: A= Ao [1+ (t/n)] ^tn

Solution:

1,000,000= 10,000 [1+ (.12/4)] ^4t

1,000,000= 10,000(1.03) ^4t
(Divide the whole equation by 10,000 in order to eliminate 10,000 from the right side of the equation)

100= (1.03)^ 4t

ln 100= 4t ln(1.03)

(ln 100/ ln 1.03) = 4t

155.7969/4= t

38.9492= t

Therefore, it will take you 38 years and 11 months to be a millionaire.

3) It is estimated that 20% of a radiactive substance decays in 30 hours. What is the half life of this substance?

Given:

A= 0.5( 50% of the substance)
Ao= 1( 100% is the original amount of the substance)
m= .80( the reate remaining after 30 hours)
t=?
p= 30 hours

Formula: A= Ao m ^(t/p)

Solution:

0.5= 1(0.8)^ (t/30)

0.5= 0.8^ (t/30)

ln 0.5= (t/30) ln 0.8

(ln 0.5)/ (ln 0.8)= t/ 30

3.1063* 30= t

93.1885 =t

Therefore, it will take 93 hours for the substance to reach its half life.

That's all for today's scride......

The next scribe will be ruschev........

See you all tomorrow guys!!!!!!!

God bless you all!!!!!