The height of a firework is modeled by $h(t)=u{t}^2+vt+4$, where $h$ is in metres and $t$ is in seconds. The firework reaches its maximum height of $9$ m at $t=1$ s.

The depth of water beside a pier is modelled by the function $d(t)=a\sin bt+18$, for $0\le t\le 20$, where $a>0$, $b>0$, and $t$ is the time in hours after the water level passes its mean depth while rising.

The water reaches a highest depth of 26 metres 4 hours later.

The lowest depth is 10 metres.

Lina is cycling to a campsite located 8 km from where she starts. The distance, $s$, in kilometres, that Lina has travelled from her starting point can be modelled by the exponential function $s(t)=a+b(k^{-t})$, where $t\ge 0$ and $t$ is the time in minutes since Lina started cycling.

The height of a seat on a Ferris wheel is described by the function $h(t)=a\sin bt+14$, for $0\le t\le 12$, where $a>0$, $b>0$, and $t$ represents the time in minutes after the seat passes the wheel's centre height while moving upward.

The seat reaches its highest point of 20 metres 3 minutes later.

The lowest point of the wheel is 8 metres.

The graph below shows the vertical displacement, $D$ (in metres), of a camera drone relative to the level of a bridge deck against $t$, the time in minutes after filming begins.

This data is fitted by a cubic function given by $D=a{t}^3+b{t}^2+ct+d$, where $a$, $b$, $c$ and $d$ are constants. The curve passes through the following points.

Values of $D<0$ indicate that the drone is below the level of the bridge deck.