Geometric Series Help!!!!?

Question

A city has a population of 20,000 people in the year 2000. If the population increases 5% per year, what will the population be in 2010? ( You are not summing the population over 2000-2010. Find the population in the year 2010, use a1rn to solve.)

(my main confusion is r)

Answer 1

Don't worry about r. This is the same as the
compound interest problem:
If $20000 is invested at 5% compounded annually,
what will be the amount in 10 years?
So the answer is 20000(1.05)^10 = 32577(roughly).

Answer 2

let year 2000 be the first postion number, then at 2010, the position number is 11.

the fomula for geometry is:
an = a1 * r^(n-1)

the ratio is 1.05

an = 20,000 (1.05)^(n-1)

so at yr 2010, the population is
an = 20000(1.05)^(11-1)
an = 32577

the actual number is 32577.89254 but since we can't have part of a person, so i took the whole number

Answer 3

equating basic ratios for each series, q/p = 32/q, or q² = 32p ...... (i) 4/q = p/4, or p = sixteen/q ........ (ii) substituting in (i), q³ = sixteen*32 = 8*8*8 q = 8, p = 2 ---------------