Question 1194035: In 2000, the population of Littletown was 16 thousand. Use the given doubling time to predict the population in 2060. Assume a doubling time of 30 years.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of years since 2000
y = population, in thousands, at year 2000+x
D = doubling time = 30 years
P = initial population in thousands = 16
y = P*(2)^(x/D)
y = 16*(2)^(x/30)
is the population growth equation
Notice if we plugged in x = 30 we get
y = 16*(2)^(x/30)
y = 16*(2)^(30/30)
y = 16*(2)^(1)
y = 16*(2)
y = 32
Showing the population is now 32,000 in the year 2030
Now let's plug in x = 60
y = 16*(2)^(x/30)
y = 16*(2)^(60/30)
y = 16*(2)^(2)
y = 16*(4)
y = 64
The population is now 64,000 in the year 2060
In other words, the population has doubled twice (aka quadrupled).
The first time for the timespan of 2000 to 2030
The second time for the timespan of 2030 to 2060
This is of course the predicted population and not what it is 100% guaranteed to be.
Answer: 64,000
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