To model the population decline of a city with a declining rate of 2% per year, we can start with the initial population and apply the rate of decline.
The population after x years can be modeled by the equation:
\[ y = P \cdot (1 - r)^x \]
where:
- \( P \) is the initial population (15,000 in this case),
- \( r \) is the rate of decline (2% or 0.02),
- \( (1 - r) \) is the remaining population after decline (which is \( 1 - 0.02 = 0.98 \)).
Substituting the values, we get:
\[ y = 15,000 \cdot (0.98)^x \]
Thus, the correct equation that models the population \( y \) after \( x \) years is:
\[ y = 15,000 \cdot (0.98)^x \]
This corresponds to the option:
y = 15,000 ⋅ (0.98)^x
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