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) \\(\bigcirc\\ y = 15,000 \cdot (98)^x\\) \\(\bigcirc\\ y = 15,000 \cdot (2)^x\\) \\(\bigcirc\\ y = 15,000 \cdot (0.98)^x\\) \\(\bigcirc\\ y = 15,000 \cdot 0.98x\\) graphing calculator

Explanation:

Step1: Recall exponential decay formula

The general formula for exponential decay is $y = a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay (as a decimal), and $x$ is the time.

Step2: Identify values for formula

Here, the initial population $a = 15000$, the decay rate $r = 2\% = 0.02$. So $1 - r = 1 - 0.02 = 0.98$.

Step3: Substitute into formula

Substituting $a = 15000$ and $1 - r = 0.98$ into the exponential decay formula, we get $y = 15000 \cdot (0.98)^x$.

Answer:

$y = 15,000 \cdot (0.98)^x$ (the third option)