Solve the given problem related to population growth.
A city had a population of 23,400 in 2007 and a population of 26,600 in 2012.
(a) Find the exponential growth function for the city. Use $t=0$ to represent 2007. (Round $k$ to five decimal places.)
\[
N(t)=
\]
(b) Use the growth function to predict the population of the city in 2022. Round to the nearest hundred.

Step 1 ：Given that the population in 2007 (t=0) is 23,400 and the population in 2012 (t=5) is 26,600, we can substitute these values into the formula to solve for \(k\).

Step 2 ：Using the exponential growth function \(N(t) = N_0 * e^{kt}\), where \(N(t)\) is the population at time \(t\), \(N_0\) is the initial population, \(k\) is the growth rate, and \(t\) is the time, we find that \(k\) is approximately 0.02564.

Step 3 ：Substituting the values into the exponential growth function, we get \(N(t) = 23400 * e^{0.02564t}\).

Step 4 ：To predict the population in 2022 (t=15), we substitute \(t=15\) into the function to get \(N(15)\).

Step 5 ：The predicted population of the city in 2022 is approximately \(\boxed{34300}\).