Respuesta :
Answer:
[TeX] U_n=4 X 1.13^{n-1}[/TeX]
[TeX] U_{17}=28[/TeX]
Step-by-step explanation:
Since each town he has allows him to create 1.13 times as many villagers as he had in the one before.
The population of the next village will be a multiplication of the population of the previous village by 1.13.
This forms a sequence in which the next term is obtained by multiplication of the previous term by a constant. This type of sequence us called a Geometric Sequence and the constant is called the Common ratio.
For any number of terms, the nth term of a Geometric Progression is determined using the formula:
[TeX] U_n=ar^{n-1}[/TeX]
Where a= First Term
r= common ratio
n= number of terms
The game gave Chase 4 villagers to start with.
Therefore, his first term a=4
The common ratio, r= 1.13
To predict the number of villagers in any specific town, we use the formula:
[TeX] U_n=4 X 1.13^{n-1}[/TeX]
In the 17th town, i.e. n=17
The number of villagers that can be created will be found by substituting n=17 into the formula above.
[TeX] U_{17}=4 X 1.13^{17-1}[/TeX]
[TeX] =4 X 1.13^{16}[/TeX]
[TeX] =28.27[/TeX]
Since number of villagers cannot be fractional, the number of villagers he can create to live in the 17th village is 28.
