SEWER SYSTEM $(20\%)$

The intercepting sewer of the urban$/$rural area in the previous "stormwater systems" problem has a diameter of $0\mathrm{.}6m$ and slope $1\mathrm{.}0\%($Manning$\text{'}$s $n=0\mathrm{.}015).$ Due to the development of the area there is an increase on the population as well as an increase on the water demand per capita. During May of $2024,$ the max$\frac{Q}{Q_{\text{f}\text{u}\text{l}\text{l}}}$ was $50\%$ and during May of $2014$ the max $\frac{y}{D}$ was $40\%($where $y$ is the flow depth in pipeline and $D$ is the pipe diameter$).$ Assume that the wastewater design discharge increases with time based on the following formula:

$Q(t)=b^t$

where a and $b$ are coefficients to be determined and $Q(t)$ is the wastewater discharge at time $t.$ Based on the data given, find the coefficients a and $b.$