) A water tank is emptying steadily by 2 liters of water per hour. There were 2 liters of water 6 hours after
midnight. Let x represent the number of hours since midnight, and let y represent the number of liters of water
in the tank. Find the equation showing the amount of water at time x
y(6) = 2, so
y = -2(x-6)+2 = 14-2x
for 0 <= x <= 7
To find the equation showing the amount of water at time x, we can start by determining the rate at which the water is being emptied from the tank.
Given that the water tank is emptying steadily by 2 liters of water per hour, we can express the rate of change of the amount of water in the tank with respect to time as -2 liters per hour. The negative sign indicates the decrease in the amount of water.
To find the amount of water in the tank at a specific time x, we need to consider the initial amount of water in the tank and subtract the amount of water that has been emptied.
Given that there were 2 liters of water 6 hours after midnight, we can use this information as the initial condition. So at x = 6, the amount of water in the tank, y, is 2 liters.
Now, let's write the equation using the given information:
y = initial amount of water - amount emptied
= 2 liters - (rate of emptying * time)
= 2 - (-2 * x) [because the rate of emptying is -2 liters per hour]
Simplifying the equation:
y = 2 + 2x
Therefore, the equation showing the amount of water in the tank at time x is y = 2 + 2x.