Question

a town has a population of $1.23 \times 10^4$ and grows at a rate of 6.7% every year. which equation represents the town’s population after 4 years?
answer
$p = (1.23 \times 10^4)(1.067)^4$
$p = (1.23 \times 10^4)(0.067)^4$
$p = (1.23 \times 10^4)(1 - 0.067)^4$
$p = (1.23 \times 10^4)(1.67)^4$

Explanation:

Step1: Identify growth formula

The formula for exponential growth is $P = P_0(1 + r)^t$, where $P_0$ is initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Convert percentage to decimal

Convert 6.7% to decimal: $r = \frac{6.7}{100} = 0.067$

Step3: Calculate growth factor

Growth factor is $1 + r = 1 + 0.067 = 1.067$

Step4: Plug in values

$P_0 = 1.23 \times 10^4$, $t=4$, so $P = (1.23 \times 10^4)(1.067)^4$

Answer:

$P = (1.23 \times 10^4)(1.067)^4$