For a safety device air is pump into a spherical bladder at a rate of 1000 cm^3 per second. create a differential equation and mathematical model for the diameter of the bladder at time t.
1) A small beverage company makes two brands of sports drink in the same storage tank, the “Original” and the “Reduced Sugar” version. The Reduced Sugar version has 50% of the amount of sugar of the Original version.
A constant volume of 100 gallons is maintained in the tank while switching between products. For the Original version the tank has a total of 20 lbs of sugar in solution. To switch to the Reduced Sugar version, pure water is added to the tank at 5 gallons/minute.
To switch from Reduced Sugar back to the Original version, a syrup made up 0.5lb sugar per gallon of water is added at 5 gallons/minute. The volume is remained constant at 100 gallons.
Develop 2 mathematical models to determine the amount of sugar at time (t):
a) Converting from Original to Reduced Sugar
b) Converting from Reduced Sugar to Original
How long does it take, in minutes, to convert from Original to Reduced Sugar and Reduced Sugar to original?