Question

The population of a city with 15,000 people declines at a rate of 2% each year. Which is an exponential equation that models the population, y, after x years? (1 point) Responses y=15,000⋅0.98x y is equal to 15 comma 000 times 0 point 9 8 x y=15,000⋅(2)x y is equal to 15 comma 000 times 2 to the x th power y=15,000⋅(98)x y is equal to 15 comma 000 times 98 to the x th power y=15,000⋅(0.98)x y is equal to 15 comma 000 times 0 point 9 8 to the x th power

Answer 1

The correct exponential equation that models the population \( y \) after \( x \) years, given a decline of 2% each year, is:

\[ y = 15,000 \cdot (0.98)^x \]

This equation indicates that the population starts at 15,000 and decreases by 2% (which is represented by multiplying by 0.98) for each year \( x \).