# rate problem with separation of variables

• Dec 12th 2009, 09:04 PM
shawli
rate problem with separation of variables
The rate at which a substance dissolves in a solution is proportional to the amount of the substance that is present. Thirty grams of sodium chloride are put in a litre of water , and is found that 1 hr later only 10g are left. How much will be left after 30min?

i have no idea how to do this!
• Dec 13th 2009, 12:12 AM
Diemo
Quote:

Originally Posted by shawli
The rate at which a substance dissolves in a solution is proportional to the amount of the substance that is present. Thirty grams of sodium chloride are put in a litre of water , and is found that 1 hr later only 10g are left. How much will be left after 30min?

i have no idea how to do this!

The rate of change of the substance is porportional to the amount of the substance. The instantanous rate of change in the derivitive. $N'=\alphaN$Use this to work out what the feunction for N is. Then input your numbers.
• Dec 13th 2009, 12:13 AM
Diemo
Quote:

Originally Posted by shawli
The rate at which a substance dissolves in a solution is proportional to the amount of the substance that is present. Thirty grams of sodium chloride are put in a litre of water , and is found that 1 hr later only 10g are left. How much will be left after 30min?

i have no idea how to do this!

The rate of change of the substance is proportional to the amount of the substance. The instantaneous rate of change in the derivative. $N' =\alpha N$Use this to work out what the function for N is. Then input your numbers.