Answer
year $2014$
Work Step by Step
Using $y=a\cdot b^x$, then the population of Chessville can be modeled by
$$\begin{aligned}
y&=50\,000(1+0.07)^x
\\&=
50\,000(1.07)^x
.\end{aligned}$$
On the other hand, the population of Checkersville can be modeled by
$$\begin{aligned}
y&=70\,000(1-0.04)^x
\\&=
70\,000(0.96)^x
.\end{aligned}$$
The graph below shows the graphs of the equations above. The blue graph represents the population of Chessville while the red graph represents the population of Checkersville.
Since the graphs intersect somewhere between $x=3$ and $x=4$, then the population of Chessville will first exceed the population of Checkersville $4$ years after $2010$. Hence, this will be in the year $2014$.
