Question

brainly 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.

Answer 1

Answer:

$U_n=4 X 1.13^{n-1}$

$U_{17}=28$

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:

$U_n=ar^{n-1}$

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:

$U_n=4 X 1.13^{n-1}$

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.

$U_{17}=4 X 1.13^{17-1}$

$=4 X 1.13^{16}$

$=28.27$

Since number of villagers cannot be fractional, the number of villagers he can create to live in the 17th village is 28.