Solve the Problem $\frac { d y } { d t } = 32 - \frac { 5 } { 120 + 3 t } y$

question 24

Multiple Choice

Solve the problem.
-A tank initially contains 120 gal of brine in which 40 lb of salt are dissolved. A brine containing 4 lb/gal of salt runs into the tank at the rate of 8 gal/min. The mixture is kept uniform by stirring and flows out of the tank at The rate of 5 gal/min. Write, in standard form, the differential equation that models the mixing process.

• A) \(\frac { d y } { d t } = 32 - \frac { 5 } { 120 + 3 t } y\)
• B) \(\frac { \mathrm { dy } } { \mathrm { dt } } + \frac { 5 } { 120 - 3 \mathrm { t } } \mathrm { y } = 32\)
• C) \(\frac { d y } { d t } + \frac { 5 } { 120 + 3 t } y = 32\)
• D) \(\frac { \mathrm { dy } } { \mathrm { dt } } + \frac { 8 } { 120 + 3 \mathrm { t } } \mathrm { y } = 20\)

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