Mathematics
esha1963:

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 as he had in the one before. The game gave Chase 4 villagers to start with. Explain to Chase how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in his 17th town.

esha1963:

@darkknight

darkknight:

This is very similar to the first question you asked help on. Can you tell me the useful info that they have given?

esha1963:

each town allows him to create 1.13 villagers more than the previous and 4 villagers to start with

esha1963:

1.13 times villagers^ sorry

esha1963:

and we have to create an equation and find villagers in his 17th town

darkknight:

perfect, so 1.13 would be our slope and we would have a coordinate at (1,4) I can see that this is different than the way that you have been doing but this is the method for algebra and it teaches you some useful formulas so lets do it this way: So now we can set up our point-slope equation

darkknight:

$(y-4)=1.13(x-1)$

darkknight:

Distribute for x and solve for y. x in this case is the village number. And y is the number of villagers

darkknight:

This equation would give you your equation in terms of villagers for the number of villages.

darkknight:

How would you approach this?

esha1963:

can we do it the way how i did the first post? or that wouldn't work?

esha1963:

can we use t=1.13v?

darkknight:

That would not work. Because you do not account for the y-intercept. we have to solve for our slope-intercept equation by first using point slope

esha1963:

where t is the # of towns and you solve for v?

esha1963:

oh okay

esha1963:

can we use the geometric series formula?

darkknight:

So the way I have been doing it is correct. Your way might be a simplified version but the way I do it has a lot of algebra skills in it. Also the geometric series formula is to find the sum of all numbers leading up to it. So that is beside the point

darkknight:

The way I have been doing it is pretty easy and simple. It also only uses basic algebra

esha1963:

okay can you teach me it your way? go through with me step by step?

darkknight:

esha1963:

so i would replace x with 17?

esha1963:

and solve for x?

darkknight:

So the equation i got, do you understand how I got it?

darkknight:

So you want to solve for y, and set the equation in terms of y. Just a slope intercept equation in the form of y=mx+b

esha1963:

yes you used the x,y coordinate

darkknight:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @darkknight $(y-4)=1.13(x-1)$ $$\color{#0cbb34}{\text{End of Quote}}$$ So that is the equation. And we want to solve for y y-4=1.13x-1.13 Add 4 to both sides y=1.13x + 2.87 Then plug in 17 for x

esha1963:

oooohhh. now i understand.

esha1963:

now that makes sense. thank you so much!

darkknight:

Np

esha1963:

y would be 22.08 right?

darkknight:

Yes, we can round down to 22 because we can't have .08th of a villager.

esha1963:

yes i was just about to say that lol

esha1963:

so 22 villagers in his 17th village

darkknight:

Yeah

esha1963:

thanks!!

darkknight:

np

esha1963:

i got this wrong :( but the answer was an = 4(1.13)^n – 1 a17 = 4(1.13)^17 – 1 a17 = 28.269 28 villagers