9. (a) Use the substitution \(u = 4 - \sqrt { } x\) to find $$\int \frac { \mathrm { d } x } { 4 - \sqrt { } x }$$ A team of scientists is studying a species of slow growing tree.
The rate of change in height of a tree in this species is modelled by the differential equation $$\frac { \mathrm { d } h } { \mathrm {~d} t } = \frac { 4 - \sqrt { } h } { 20 }$$ where \(h\) is the height in metres and \(t\) is the time measured in years after the tree is planted.
(b) Find the range in values of \(h\) for which the height of a tree in this species is increasing.
(c) Given that one of these trees is 1 metre high when it is planted, calculate the time it would take to reach a height of 10 metres. Write your answer to 3 significant figures.
\includegraphics[max width=\textwidth, alt={}, center]{5b698944-41ac-4072-b5e1-c580b7752c39-31_154_145_2599_1804}