Question

suppose a city with population 300,000 has been growing at a rate of 6% per year. if this rate continues, find the population of this city in 18 years. the population in 18 years will be approximately \square. (round to the nearest whole number as needed.)

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $P(t) = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the annual growth rate (in decimal), and $t$ is the time in years.
Here, $P_0 = 300000$, $r = 0.06$ (since 6% = 0.06), and $t = 18$.

Step2: Substitute the values into the formula

$P(18) = 300000 \times (1 + 0.06)^{18}$

First, calculate $(1 + 0.06)^{18}$. Using a calculator, $(1.06)^{18} \approx 2.854339153$

Step3: Multiply by the initial population

$P(18) = 300000 \times 2.854339153$
$P(18) \approx 856301.7459$

Step4: Round to the nearest whole number

Rounding $856301.7459$ to the nearest whole number gives 856302.

Answer:

856302