To model the population of a city that declines at a rate of 2% each year, we need to express the decline as a multiplier.
A decline in the population by 2% means that each year, 98% of the population remains. This can be represented as a multiplier of \(0.98\) (which is equal to \(1 - 0.02\)).
The general formula for exponential decay is:
\[ y = P \cdot (1 - r)^x \]
where:
- \(P\) is the initial population,
- \(r\) is the rate of decline,
- \(x\) is the number of years,
- \(y\) is the population after \(x\) years.
For this specific case:
- \(P = 15,000\),
- \(r = 0.02\), so \(1 - r = 0.98\).
Putting this together, we get:
\[ y = 15,000 \cdot (0.98)^x \]
Therefore, the correct answer is:
\[ y = 15,000 \cdot (0.98)^x \]
So, the correct option from your list is:
y = 15,000 ⋅ (0.98)^x.