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Saturday, May 27, 2006

Last Scribe of year

Today, acually friday, we had a sub for both classes.

In the morning we worked in groups on a group assignment, about Logarithm word problems.
The question on the assignment was:

Sugar is put into a large quantitiy of water and the mixture is stirred. After 2 minutes 50% of the sugar had dissolved. How much longer will it take until 90% of the sugar has dissolved (Model the sugar dissolving as an exponential decay function.) ?

What we know :
Original = 100%
This is 100% because when we begin the experiment none of the sugar has dissolved, therefore there was still 100% in the mixture.
Final = 10%
This is 10% because we want to know how much time it will take 90% of sugar to become dissolved leaving 10% of the sugar left.
Life = 1/2
This is because we know that after every 2 minutes of the experiment 50% of the sugar will be dissolved which is also known as a half-life.

With that information we plug it into the equation:
0.1 = 1 ( 1/2) t/2

0.1 Represents the the final which is 10%
1 Represents the initial which is 100%
1/2 Represents the life which is 50%
2 Represents the amount of time it will take for the life to decay

0.1 = 1 ( 1/2) t/2
0.1 = (1/2) t/2
ln 0.1 = (t/2) (ln 1/2)
(ln 0.1) / (ln 1/2) = t/2
2 ((ln0.1) / (ln 1/2)) = t
6.6439 = t
It will take approximately 7 minutes for 90% of the sugar to become dissolved in water.

*NOTE: I am not sure if this is the right answer as we did not go over it in class, but it is what the majority of the class got so i'm assuimg it is.

After the group assignment we did some questions from out text book for the rest of the period.
Pg. 83 Questions 30 - 34

In the afternoon we just did questions in our text book for the period.
Pg. 119 Questions 1 - 33 Odd

That was all we did for friday's class. Last scribe of the year and I get a not so bad one =D. Anyway monday's scribe is Jefferson haha who better carry out our plan for next week =P.

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