SOLUTION:
The initial population of a town is
37003700​,
and it grows with a doubling time of 10 years. What will the population be in
1212
​years?
What will the p
Algebra.Com
Question 1089681:
The initial population of a town is
37003700,
and it grows with a doubling time of 10 years. What will the population be in
1212
years?
What will the population be in
1212
years?
nothingm
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
not sure how many years you really mean, but here's the formula.
f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
you say the population doubles every 10 years.
your time period is therefore 10 years and your growth rate is 100% = 1.0
the formula becomes:
f = p * (1 + 1) ^ n
simplify this to get f = p * 2 ^ n
your starting population figure is 3700.
your number of years is 12.
since your time period is every 10 years, then n = 12/10 = 1.2
the formula becomes f = 3700 * 2 ^ 1.2.
solve for f to get f = 8500.367827
there's another way to solve it that you might find easier to understand.
if the population doubles every 10 years, then the annual growth rate can be calculated as follows:
f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the annual growth rate
n is the number of years.
if the population doubles every 10 years, then the formula becomes:
2 = 1 * (1 + r) ^ 10
this is equivalent to 2 = (1 + r) ^ 10 since the 1 * can be removed because 1 * anything is equal to anything just by itself.
so your formula to solve for the growth rate per year becomes:
2 = (1 + r) ^ 10
take the 10th root of each side of this equation to get:
2^(1/10) = 1 + r
solve for r to get r = 2^(1/10) - 1 = .071773463
go back and solve your problem using an annual growth rate instead of a 10 years growth rate.
your formula becomes f = 3700 * (1 + .071773463) ^ 12
f is the future value.
your annual growth rate if .071773463
the number of years is 12
solve for f to get f = 8500.367827
this is the same answer as before as it should be.
i'll be available to answer any questios you might have on this.
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