The correct exponential equation that models the population \( y \) after \( x \) years for a city with an initial population of 15,000 that declines at a rate of 2% each year is:
\[ y = 15,000 \cdot (0.98)^x \]
This is because a decline of 2% means that each year, 98% of the population remains (100% - 2% = 98%). Thus, the population can be described by multiplying the initial population by \( 0.98 \) raised to the power of \( x \), which represents the number of years.
So, the response is:
y = 15,000⋅(0.98)ⁱ