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 eight 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

it appears that the number of villagers in brian's game for 0 towns is 8.

for 1 town, it is 8·1.17

for 2 towns, it is 8·1.17·1.17 = 8·1.17²

for 3 towns, it is 8·1.17·1.17·1.17 = 8·1.17³

apparently, for n towns, the number of villagers in brian's game is 8·1.17ⁿ. this expression can be put into an equation that expresses the number of villagers (v) as a function of n:

v(n) = 8·1.17ⁿ . . . equation to predict villagers for n towns

for 16 towns, we can substitute the value 16 for n to find the number of villagers.

v(16) = 8·1.17¹⁶ ≈ 99 villagers

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)