a. Let's start by defining the initial population $P_0$ as 737,000, and the annual growth rate $r$ as 2% or 0.02. Then, the exponential function that represents the population after $t$ years can be written as:
$$y = P_0 (1 + r)^t$$
Substituting the values, we get:
$$y = 737{,}000(1 + 0.02)^t$$
Simplifying this expression, we get:
$$y = 737{,}000(1.02)^t$$
b. To find the population after 14 years, we can simply substitute $t=14$ into the exponential function we derived in part (a):
$$y = 737{,}000(1.02)^{14} \approx 1{,}064{,}535$$
Rounding to the nearest thousand, we get:
$$y \approx 1{,}064{,}000$$
Therefore, the population of the city after 14 years is estimated to be about 1,064,000.