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⋅(2)x
y is equal to 15 comma 000 times 2 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

y=15,000⋅0.98x
y is equal to 15 comma 000 times 0 point 9 8 x

y=15,000⋅(98)x
y is equal to 15 comma 000 times 98 to the x th power

Answer 1

y = 15,000·(0.98)^x

Reason: a 2% annual decline multiplies the population by 1 − 0.02 = 0.98 each year, so y = 15000(0.98)^x.