Mathematical Methods · Unit 1 · Binomial expansion and cubic functions · Cubic functions
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A water tank initially contains 1,200 litres. Water drains from the tank such that the total volume drained after $t$ hours is modelled by the cubic function $d(t) = 0.5t^3 - 6t^2 + 18t$, where $0 \leq t \leq 8$. The graph of $d(t)$ is shown below. At which value of $t$ is the drainage rate instantaneously zero?
A storage tank is being filled with water. The volume of water V (in cubic metres) in the tank at time t (in hours) is modelled by the cubic function V(t) = 2t³ - 9t² + 12t, where 0 ≤ t ≤ 3. Determine the time at which the rate of flow into the tank is at a minimum.
A storage tank for a warehouse is modelled by the cubic function $h(t) = -0.5t^3 + 3t^2 + 10t + 4$, where $h(t)$ is the height of liquid in metres and $t$ is the time in hours after the tank begins filling. Determine the height of liquid in the tank at $t = 2$ hours.