Sugar Concentration in a Tank

The video tutorial explains a problem involving a mixing tank with water and sugar. It starts with defining functions for the amount of water and sugar over time, leading to a function for concentration. The tutorial calculates the concentration of sugar in the tank after 8 minutes and compares it to the initial concentration, concluding that the concentration decreases over time.

What is the initial amount of sugar in the tank?

• 50 pounds

• 40 pounds

• 30 pounds

• 20 pounds

At what rate is water added to the tank?

• 25 gallons per minute

• 20 gallons per minute

• 15 gallons per minute

• 10 gallons per minute

What is the function for the amount of water in the tank after T minutes?

• W(t) = 200 + 10t

• W(t) = 200 + 15t

• W(t) = 200 + 20t

• W(t) = 200 + 25t

How is the function for the amount of sugar in the tank defined?

• S(t) = 40 + 3t

• S(t) = 40 + 4t

• S(t) = 40 + 2t

• S(t) = 40 + 1t

What is the formula for the concentration of sugar in the tank?

• C(t) = (40 + 2t) / (200 + 10t)

• C(t) = (40 + 2t) / (200 + 15t)

• C(t) = (40 + 3t) / (200 + 15t)

• C(t) = (40 + 4t) / (200 + 15t)

After 8 minutes, what is the concentration of sugar in the tank?

• 0.175 pounds per gallon

• 0.200 pounds per gallon

• 0.150 pounds per gallon

• 0.125 pounds per gallon

What is the simplified ratio of sugar to water after 8 minutes?

• 7 pounds per 30 gallons

• 7 pounds per 35 gallons

• 7 pounds per 40 gallons

• 7 pounds per 45 gallons

What is the initial concentration of sugar in the tank?

• 0.1 pounds per gallon

• 0.2 pounds per gallon

• 0.4 pounds per gallon

• 0.3 pounds per gallon

How does the concentration after 8 minutes compare to the initial concentration?

• It is greater

• It is the same

• It cannot be determined

• It is less

What is the greatest common factor used to simplify the concentration ratio after 8 minutes?

• 8

• 10

• 4

• 6