Question

Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as many villagers. The game gave Chase 4 villagers to start with. Help Chase expand his empire by solving for how many villagers he can create with 17 towns. Then explain to Chase how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.

Answer 1

i just want to check my answer i know the formula is an=a1 * r^(n-1)

Answer 2

so a17= 4 * 1.13^(17-1)

Answer 3

a17 = 4* 1.13^6
a17= 4*7.067325527
a17= 28.269 .. final answer

Answer 4

\[a_2 = a_1 \times r^n\]where a1 = 4 (beginning state), r = 1.13 (ratio), n = 17 (# of towns).
Imagine having only one town - with your formula you would have been stuck at 4 constantly. What you have probably thought about is the progress in time, which is not this case.
\[a_i = a_1 \times \left( r^n\right)^\left(i-1\right)\]
where i is # of time units which the ratio is related to.

Answer 5

For 17 towns it makes 31.94 guys - you should think about rounding to 32 guys ;)

Answer 6

i thought that because they gave me the first term and told me how many villagers with town 17 so i thought i'm solving for a number that is increasing from town 1 that has 4 villagers to town 17

Answer 7

how did you get that? i don't understand what i'm solving for

Answer 8

Each town increases the ratio by 1.13
2 towns by 1.13^2
3 towns by 1.13^3...
17 towns by 1.13^17
that is what the 1st formula is for:\[a_2 = 4 \times 1.13^{17} = 31.944\]around 32 guys will be there after one turn with 17 towns.

Answer 9

yes and that's exactly how i solved it but the formula that i have is an=a1* r^(n-1) and i got 28.269 but your formula is different you didn't have r^(n-1)

Answer 10

but i understand what you did and i exactly solved it with the same process

Answer 11

the formula with ^(n-1) or ^(i-1) in the one I listed - it would be like:
1st day there are 4 guys - r^(1-1) = r^0
2nd day there are 32 guys - ^(2-1) = r^1
3rd day 255 guys - r^(3-1) = r^2
in another words, the ratio in your formula is not the r = 1.13, but the r^n = 1.13^17 = 7.986

See the difference? What you are expected to do is just to find the ratio usig 17 towns. The formula you wrote represents progress in time with given ratio.

Answer 12

i thought your formula solves for a progress in time too @Frouzen

Answer 13

i just got confused with which one to use and how can i know the difference in the problem that i can know i need to use this one not yours for example

Answer 14

http://prntscr.com/6vmtog

Answer 15

As you probably can see, this is an example of exponencial growth, where the formula \[a_n = a_1 \times r^{n-1}\] represents # of villagers after n days/years/whatever.
The ratio itself is afflicted by the 17 towns stuff. If you were asked "how many villagers will be there with 17 towns after 5 turns", that would be the case of your formula.

Answer 16

https://answers.yahoo.com/answer?offset=r1426096598~r%3A0&sid=&isCategory=0
this might help as well

Answer 17

oh ok i see now @Frouzen , thank you so much for your help and patient and for writing our the formulas for me ..

Answer 18

thank you @SyedMohammed98 ..

Answer 19

You're Welcome

Answer 20

If you are done @DoShKa_SyRiA could you close this question?