SOLUTION: it is estimated that the population of a village increases by 10 percent every five years. if the population of the village is 150,000 this year, what will be the estimated populat

Question 1160871: it is estimated that the population of a village increases by 10 percent every five years. if the population of the village is 150,000 this year, what will be the estimated population ten years from now?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the population increases by 10% evey five yhears.
f = p * (1 + r) ^ n
f is the future value
p is the presnt value
r is the interest rate per time period
n is the number of time periods.
the time periods are every 5 years.
the formula becomes:
f = 150,000 * (1 + .10) ^ 2
solve for f to get:
f = 181,500.
that's your solution.
in 10 years, there are 2 five year periods, therefore n = 2.
if you wanted to solve for the annual growth rate in this problem, you would do the following.
p = 1
f = 1.10
r = (1 + r)
n = 5
formula becomes:
1.1 = 1 * (1 + r) ^ 5
this becomes 1.1 = (1 + r) ^ 5
take the fifth root of both sides of this equation to get:
1.1 ^ (1/5) = 1 + r
subtract 1 from both sides of this equaation to0 get:
1.1 ^ (1/5) - 1 = r
solve for r to get:
r = .0192448765.
that's the annual growth rate.
with your time periods in years, rather than every 5 years, f = 150,000 * (1 + .0192448765) ^ 10 gets you:
f = 181,500.
same answer, as it should be if you did everything correctly.

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