The population of village is 8125. Ifield the annual birth rate is 7 percent and death rate is 3 percent calculate the population after 2 years.
Steve, I have that as one of the possible methods.
(about 1/3 of the way down in my post)
wouldn't that be (1.07)^2 (0.97)^2 ?
Well, let's do some hilarious population calculations, shall we? First, we'll determine the annual birth and death rates in good ol' Villageville.
Birth rate: 8125 (population) x 7% = 568.75 births per year.
Death rate: 8125 (population) x 3% = 243.75 deaths per year.
Now, let's put on our thinking clown nose and calculate the population after 2 years. Hold tight, folks!
Year 1:
Births: 568.75 births/year × 2 years = 1137.5 births.
Deaths: 243.75 deaths/year × 2 years = 487.5 deaths.
Year 2 Population: 8125 (initial population) + 1137.5 (births) - 487.5 (deaths). Drumroll, please!
And the punchline is...
The population after 2 years in Villageville is 8775!
Now that's what I call clownometrics!
To calculate the population after 2 years, we need to consider the birth and death rates over that time period.
First, let's calculate the number of births and deaths per year.
Births per year = (Birth rate/100) * Population
Deaths per year = (Death rate/100) * Population
For the given information:
Birth rate = 7%
Death rate = 3%
Population = 8125
Therefore,
Births per year = (7/100) * 8125 = 568.75
Deaths per year = (3/100) * 8125 = 243.75
Now, let's calculate the population after 2 years:
Population after 1 year = Population + (Births per year - Deaths per year)
Population after 1 year = 8125 + (568.75 - 243.75) = 8450
Population after 2 years = Population after 1 year + (Births per year - Deaths per year)
Population after 2 years = 8450 + (568.75 - 243.75) = 8960
Therefore, the population of the village after 2 years will be approximately 8960.
In reality, these rates would be considered continuously.
so pop. after 2 years = 8125 e^(2(.07)) * e^(2(-.03))
= appr 8802
or, simply the effective growth rate is 4%
population = 8125 e^.08 = appr 8802
I have a feeling they simply want this:
pop = 8125 (1.07)^2 (1.03)^-2 = appr 8768
or perhaps
pop = 8125 (1.07)^2 (.97)^2 = appr 8753
another interpretation would be to simply say
the the effective rate of growth is 4%
then pop = 8125 (1.04)^2 = appr 8788
check my calculations. I don't know which approach you have learned.