What does the y-intercept of this function represent?

Take a look at the graph. We can see that the horizontal axis tells us the number of years since the city was founded. 

Y-intercepts happen at x = 0. So, let's think about what x = 0 means on the graph. This would be "0 years since the city was founded" or the same time the city was founded.

In other words, the y-intercept of this function represents the initial population (the population when the city was first founded).

If you make it a little more clear i can answer it