Question

suppose a city with population 200,000 has been growing at a rate of 7% per year. if this rate continues, find the population of this city in 21 years.

the population in 21 years will be approximately □ (round to the nearest whole number as needed.)

Explanation:

Step1: Recall exponential growth formula

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

Step2: Identify given values

$P_0 = 200000$, $r = 0.07$, $t = 21$

Step3: Substitute values into formula

$P(21) = 200000 \times (1 + 0.07)^{21}$

Step4: Calculate the growth factor

First compute $(1.07)^{21} \approx 4.140562$

Step5: Compute final population

$P(21) \approx 200000 \times 4.140562 = 828112.4$

Step6: Round to nearest whole number

Round $828112.4$ to the nearest integer, which is $828112$.

Answer:

828112