The depth of water, \(d\) metres, at a harbour entrance is modelled by \(d=0.1t^3-1.2t^2+3.3t+4\), where \(t\) is the number of hours after 6 am, for \(0\leq t\leq8\).
The table shows some values of d.
| \(t\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|
| \(d\) | 4 | 6.2 | 6.6 | | 4.4 | 3.0 | 2.2 | 2.6 | 4.8 |
Complete the table of values.[1]
On the grid, draw the graph of d against t.[3]
By drawing a tangent, find the gradient at \(t=5\).[2]
Use your graph to find the minimum depth of water at the harbour entrance.[1]
Use your graph to find the values of t for which the depth of water is decreasing.[1]
A cargo ship is being loaded at the quay. As loading continues, the depth of water the ship needs is modelled by \(d=0.2t+2\).
By drawing the line \(d=0.2t+2\) on your grid, find the time by which the ship must leave in order to avoid becoming stranded. Give your answer as a time of day.[2]