Question 1160871
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.