The rate at which salt dissolves in water is directly proportional to the amount that remains un-dissolved. If ten pounds of salt is placed in a container of water and four pounds dissolves in twenty minutes, how much longer long will it take for two more pounds to dissolve? Answer: About 15.9 minutes.
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The rate at which salt dissolves is directly proportional to the amount that remains un-dissolved. This can be expressed as: \[ \frac{dS}{dt} = -kS \] where \( S \) is the amount of salt remaining, \( t \) is time, and \( k \) is the proportionality constant. Show more…
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