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⋅(98)x y is equal to 15 comma 000 times 98 to the x th power y=15,000⋅(2)x y is equal to 15 comma 000 times 2 to the x th power y=15,000⋅0.98x y is equal to 15 comma 000 times 0 point 9 8 x y=15,000⋅(0.98)x

Answer 1

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