Water is draining from a large tank. After t min, there are 150000-7500t+t^2 litres of water in the tank.?

Question

a) Determine the average rate at which the water empties from the tank in the interval between
5 and 10 minutes.
b) Determine the average rate at which the water empties from the tank in the interval between
9 and 10 min.
c) Estimate the rate at which the water runs out after exactly 10 min.
d) How much water is in the tank at exactly 10 min?

Answer 1

(a) that would be the slope of the line between the two points on the graph of f(t) as given:

(f(10)-f(5))/(10-5)
plug in your t values

(b) same thing, different interval

(c) pick a small interval centered at t=10, such as [9.9,10.1]

(d) naturally, that will be f(10)