Respuesta :
Answer:
Step-by-step explanation:
a sub n = a sub 1 x r ^ n-1
a sub n = 17 since that's what's in question
a sub 1 = 4 since that's the starting amount
r = 1.13 since that's the difference
a sub 17 = 4(1.13) ^17-1
a sub 17 = 4(7.0673255268)
a sub 17 = 28.2693021072
a sub 17 ≈ 28.37
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The number of villagers that Chase can create to live in his 17th town is 28.27.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
A.) As it is given that the number of villagers that Chase had, in the beginning, is 4, and the number of villagers will increase at the rate of 1.13 every time Chase conquers a new village. Therefore, if Chase had n number of towns then Chase had conquered (n-1) number of towns because Chase already had 1 village in the beginning, thus, the villagers will increase (n-1) number of times by the rate of 1.13 times. Therefore, the equation can be written as,
[tex]A = 4(1.13)^{(n-1)}[/tex]
Thus, the function that represents the number of villagers when chase conquered n number of villages is [tex]A = 4(1.13)^{(n-1)}[/tex].
B.) We already know the function that represents the number of villagers, therefore, the number of villagers when Chase had conquered 17 villages can be written as,
[tex]A = 4(1.13)^{(n-1)}\\\\A = 4(1.13)^{(17-1)}\\\\A = 28.27[/tex]
Hence, the number of villagers that Chase can create to live in his 17th town is 28.27.
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