College Algebra & Trigonometry, 2018a

3.1. EXPONENTIAL AND LOGISTIC APPLICATIONS 159
13) Continuous Mixing
A 100 gallon tank of pure water has salt water with 0.5 lb per gallon added to
it at a rate of 2 gallons per minute. The brine solution is mixed thoroughly and
drained at rate of 2 gallons per minute.
The equation for how many pounds of salt are in the tank at time t is given by:
y =50− 50e −0.02t
where y is measured in pounds and t is measured in minutes.
a) How many pounds of salt are in the tank after 20 minutes?
b) How long does it take for there to be 30 lbs of salt in the tank?
Round your answer to the nearest tenth of a minute.
14) Continuous Mixing
A 20 gallon tank of pure water has salt water with 0.4 lb per gallon of salt added
to it at a rate of 3 gallons per minute. The brine solution is mixed thoroughly and
drained at rate of 3 gallons per minute.
The equation for how many pounds of salt are in the tank at time t is given by:
y =8− 8e −0.15t
where y is measured in pounds and t is measured in minutes.
a) How many pounds of salt are in the tank after 15 minutes?
b) How long does it take for there to be 6 lbs of salt in the tank?
Round your answer to the nearest tenth of a minute.