Question

Help with a word problem?

Answer 1

how far have you gotten?

Answer 2

how many people does he start with?

Answer 3

so lets say: t1 = 8

when he adds a villiage, how many more people does he get?

Answer 4

*adds a town .... but yeah

Answer 5

lets keep it simple, to see a pattern develop ... hopefully

t1 = 8
t2 = 8(1.17)
t3 = 8(1.17)(1.17)
t4 = 8(1.17)(1.17)(1.17)

each town is just 1.17 more than what he had right?

Answer 6

t5 will be 8 * 4 multiples of (1.17)
t6 will be 8 * 5 multiples of (1.17)

tn will be 8 * (n-1) multiples of (1.17)

\[\large t_n=8(1.17)^{n-1}\]
seems like a fair enough rule

Answer 7

this would be the equation for the number of villagers for, n number of towns.

when tn = 16, we can solve for n right?

Answer 8

\[16=8(1.17)^{n-1}\]
\[2=(1.17)^{n-1}\]
\[2(1.17)=(1.17)^n\]
\[log[2(1.17)]=n~log(1.17)\]
\[\frac{log[2(1.17)]}{log(1.17)}=n\]

Answer 9

good luck :)

Answer 10

using a calculator would be best yes

Answer 11

youre welcome