Answer:
8 × (1.17)^t
99 villagers
Step-by-step explanation:
Given the information:
Each town Brian has allows him to create 1.17 times as many villagers as he had in the town before.
The initial number of villagers to start with = 8
To predict the number of villagers in any specific town :
Initial number × (Increment)^number of town
Let number of town = t
Increment = 1.17
Initial number (I) = 8
Hence,
8 × (1.17)^t
Using the formula :
Number of villagers in 16th town:
t = 16
Number of villagers :
8×(1.17)^(16)
8×(1.17)^16
8 × 12.33030
= 98.642
= 99 (nearest whole number)
Then the equation to solve for the number of villagers he can create to live in his 16th town will be given below.
[tex]A=A_o (1.17)^{16}[/tex]
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
Brian has been playing a game where he can create towns and help his empire expand.
Each town he has allows him to create 1.17 times as many villagers as he had in the town before.
The game gave Brian 8 villagers to start with.
Then the equation of the number of villagers will be
Let t be the town, A₀ be the initial population and A is the final population then we have
[tex]A = A_o (1.17)^t[/tex]
The number of villagers in the 8th town will be
[tex]A = A_o (1.17)^8[/tex]
Then the equation to solve for the number of villagers he can create to live in his 16th town will be
[tex]A=A_o (1.17)^{16}[/tex]
More about the exponent link is given below.
https://brainly.com/question/5497425
