A swimming pool is being emptied and the amount of water remaining in the pool after t minutes after emoting commences is given by:
Time t (min) Volume V (L)
0 30000
20 28800
40 25200
60 19200
80 10800
Find the equation describing the volume of water remaining at any time. [Hint Let V=a-b(t squared)
To find the equation describing the volume of water remaining at any time, we can use the given data points and the hint provided.
Let's assume the equation is of the form V = a - b(t^2), where V represents the volume of water remaining at time t.
Using the data points given, we can substitute the values for V and t into the equation and solve for the constants a and b.
Substituting the first data point (t=0, V=30000) into the equation:
30000 = a - b(0^2) => 30000 = a
Substituting the second data point (t=20, V=28800) into the equation:
28800 = 30000 - b(20^2) => 28800 = 30000 - 400b => 400b = 1200 => b = 3
Now we have the values for a and b. Thus, the equation describing the volume of water remaining at any time is:
V = 30000 - 3(t^2)