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

y=15,000⋅(2)x
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
=
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

Answer 1

The correct exponential equation that models the population \( y \) after \( x \) years, given that the population 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, which is represented as \( 0.98 \).

So, the response is:

**y = 15,000 ⋅ (0.98)^x**