Final answer:
The concentration of salt in the tank after t minutes is given by the function C(t) = 375t / (9000 + 25t), which accounts for the continuous addition of a brine solution containing 15 g/L of salt at a rate of 25 L/min into a tank initially containing 9000L of pure water.
Step-by-step explanation:
To calculate the concentration of salt in the water after t minutes, we need to consider the amount of brine being added to the tank and the rate at which it is being added. Since the brine has a concentration of 15 g of salt per liter, and it is being pumped into the tank at 25 L/min, we can find the amount of salt added per minute by multiplying the two:
- 15 g/L × 25 L/min = 375 g/min
This means that every minute, 375 grams of salt are being added to the tank. After t minutes, the total amount of salt in the tank is t × 375 g. The volume of the solution in the tank is the initial volume plus the volume of brine added, which is 9000 L + 25t L. The concentration of salt C(t) at any time t is given by the ratio of the total mass of salt to the total volume of the solution:
C(t) = (Salt mass added)/(Initial volume + Volume added)
= (t × 375 g)/(9000 L + 25t L)
Therefore, the concentration of salt in grams per liter after t minutes is given by the function:
C(t) = 375t / (9000 + 25t)