Question

a town has a population of $1.239 \times 10^5$ and shrinks at a rate of 9.4% every year. which equation represents the towns population after 7 years?
answer
$\bigcirc$ $p = (1.239 \times 10^5)(1 - 0.094)^7$
$\bigcirc$ $p = (1.239 \times 10^5)(1 + 0.094)^7$
$\bigcirc$ $p = (1.239 \times 10^5)(1.094)^7$
$\bigcirc$ $p = (1.239 \times 10^5)(0.06)^7$

Explanation:

Step1: Identify decay formula

The general formula for exponential decay is $P = P_0(1 - r)^t$, where $P_0$ is initial population, $r$ is decay rate, $t$ is time.

Step2: Plug in given values

$P_0 = 1.239 \times 10^5$, $r = 0.094$, $t = 7$. Substitute into formula:
$P = (1.239 \times 10^5)(1 - 0.094)^7$

Step3: Match with options

Compare the derived equation to the provided choices.

Answer:

$P = (1.239 \times 10^5)(1 - 0.094)^7$