To solve this problem, we would use the following mathematical formula for exponential growth:
P = P0 * e^(rt)
P is the final population, P0 is the initial population, r is the growth rate and t is the time in years.
First, we identify all the parameters given in this problem:
P0, the initial population, is given to be 200,000.
r, the rate of growth, is given to be 4% or 0.04 in decimal terms.
t, the time span for which we're considering the growth, is given to be 25 years.
After acquiring all the values needed for our calculation, we can now substitute them into our formula in order to get the population of the city in 25 years.
Let's perform the substitution:
P = 200,000 * e^(0.04 * 25)
We then calculate the value to get:
P = 543656.365691809
Therefore, we would expect the city's population to be approximately 543,656 if it continues to grow at this rate for 25 years.