Brian has been playing a game where he can create towns and his empire expand. each town he has allows him to create 1.17 times as many villagers. the game gave brian 8 villagers to start with. brian expand his empire by solving for how many villagers he can create with 16 towns. then explain to brian how to create an equation to predict the number of villagers for any number of towns. show your work and use complete sentences.

You can make an equation of f(n)= 8 * 1.17n, where f(n) is the total number of villagers, 8 is the starting amount of villagers, and 1.17n is the exponent of how many villagers Brian can create. If you substitute 16 into the equation, you will get how many villagers he can create with 16 towns.

f(n) = 8 * 1.17n

f(16) = 8 * 1.17n

f(16) = 8 * 12.330...

f(16) = 98.64243...

Since you cannot have a part of a villager, Brian can create about 98 villagers.

f(n) = 8 x 1.17^(n)

f(16) = 8 x 1.17^(16)

f(16) = 8 x 12.330...

f(16) = 98.64243...

This is right because

8 x 1.17 = 9.36

9.36 x 1.17 = 10.9512

10.9512 x 1.17 = 12.812904

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)