The height, \(h\) cm, of a plant is modelled by \(h=\frac{80}{1+10e^{-0.4t}}\), where \(t\) is the number of months after the first observation.
Show that \(h\) is an increasing function.[3]
Find the value of \(t\) when the height of the plant first exceeds four times its initial observation.[3]
The height, \(y\) cm, of another species of plant, \(t\) months after the first observation is given by \(y=\frac{1}{a+be^{-t}}\), where \(a\) and \(b\) are constants. Explain clearly how a straight line graph can be drawn to represent this relationship. You should state which variables should be plotted on each axis and explain how the values of \(a\) and \(b\) can be calculated.[4]