(Solved):   A. A tank contains \( 40 \mathrm{lb} \) of salt dissolved in 600 gallons of water. A salt ...

 

A. A tank contains \( 40 \mathrm{lb} \) of salt dissolved in 600 gallons of water. A salt solution containing \( 1 / 2 \mathrm{lb} \) of salt per gallon enters the tank at the rate of \( 4 \mathrm{gal} / \mathrm{min} \), and the well-stirred mixture leaves the tank at the same rate. a) Find the amount of salt \( y(t) \) in the tank at time \( t \) b) When will the salt solution leaving the tank have a concentration of \( 170 \mathrm{lb} \) per gallon? c) Find \( \lim _{t \rightarrow \infty} y(t) \) B. Suppose that a cup of hot chocolate cooled from \( 90^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) after \( 10 \mathrm{~min} \) in a room whose temperature is \( 20^{\circ} \mathrm{C} \). a) How much longer will it take the hot chocolate to cool to \( 35^{\circ} \mathrm{C} \) ? b) Instead of being left to cool at room temperature, after the initial 10 minutes the cup of \( 90^{\circ} \mathrm{C} \) hot chocolate was taken outdoors in winter where it was \( -15^{\circ} \mathrm{C} \). How long did it take to cool to \( 35^{\circ} \mathrm{C} \) ?