The variables $x$ and $y$ are connected by the relationship

Sketch the graph of ${\log }_{10}y$ against ${\log }_{10}x$. Clearly label the coordinates of the points of intersection of the graph with the coordinate axes.

A population of microbes $N$ increases over time $t$ hours according to the model $N=a{b}^t$, where $a$ and $b$ are positive constants. A scientist plots the linear relationship between ${\log }_{9}N$ and $t$. The resulting line has a positive gradient and passes through the points $(0,2.5)$ and $(-10,0)$. Determine the exact values of $a$ and $b$.