A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content. If after hours the towel has lost % of its original moisture content, after how long will it have lost %?
t=____ hours
A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content. If after hours the towel has lost % of its original moisture content, after how long will it have lost %?
t=____ hours
where k is the rate, and y is the proportion of the moisture.
so,
Integrate both sides:
You will get:
..................(1)
Use this equation to find out what your question is asking. First start with time to find out . At time , the towel
has not lost any moisture. That means
So,
Now find k. To find k, use the first part of your question.
At time , the moisture lost is 10%. So the remaining moisture in the towel is .
So,
Now, that you have and , find .
Let be the time when 70% moisture is lost, that is, the remaining moisture is 30. So, use equation (1) in a similar manner to find the time(t).