a town has a population of 9000 and grows at 3% every year. what will be the population after 9 years, to…
a town has a population of 9000 and grows at 3% every year. what will be the population after 9 years, to the nearest whole number?
Answer
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 growth rate (in decimal), and $t$ is the time in years.
Step2: Convert the growth rate to decimal
The growth rate $r = 3% = 0.03$.
Step3: Substitute the values into the formula
We have $P_0 = 9000$, $r = 0.03$, and $t = 9$. So $P(9)=9000(1 + 0.03)^9$.
Step4: Calculate $(1 + 0.03)^9$
First, calculate $1.03^9\approx1.30477319$.
Step5: Calculate the population
Multiply by the initial population: $P(9)=9000\times1.30477319\approx11742.9587$.
Step6: Round to the nearest whole number
Rounding $11742.9587$ gives $11743$.