13. A treatment is used to reduce the concentration of nitrate in the water in a pond. The concentration of nitrate in the pond water, \(N \mathrm { ppm }\) (parts per million), is modelled by the equation
$$N = 65 - 3 \mathrm { e } ^ { 0.1 t } \quad t \in \mathbb { R } t \geq 0$$
where \(t\) hours is the time after the treatment was applied.
\section*{Use the equation of the model to answer parts (a) and (b).}
- Calculate the reduction in the concentration of nitrate in the pond water in the first 8 hours after the treatment was applied.
For fish to survive in the pond, the concentration of nitrate in the water must be no more than 20 ppm .
- Calculate the minimum time, after the treatment is applied, before fish can be safely introduced into the pond.
Give your answer in hours to one decimal place.