The formula that can be used to find the number of monkeys in the nth generation is [tex]\bold{a_n=4\times 2^{n-1}}[/tex]
What is formula?
"It is a rule that is expressed in terms of mathematical symbols."
For given question,
In the first generation there are 4 monkeys on an island.
In generation 2 there are 8 monkeys, in generation 3 there are 16 monkeys, and so on.
A.
For n = 2,
[tex]a_2=4\times (\frac{1}{2} )^{2-1}\\\\a_2=4\times \frac{1}{2}\\\\ a_2=2\\\\a_2\neq 8[/tex]
This is not required formula.
B.
For n = 2,
[tex]a_2=2\times (\frac{1}{4} )^{2-1}\\\\a_2=2\times \frac{1}{4}\\\\a_2=\frac{1}{2}\\\\a_2\neq 8[/tex]
This is not required formula.
D.
For n = 2,
[tex]a_2=2\times (4)^{2-1}\\\\a_2=2\times 4\\\\a_2=8[/tex]
For n = 3,
[tex]a_3=2\times (4 )^{3-1}\\\\a_3=2\times 16\\\\a_3=32[/tex]
This is not required formula.
C.
For n = 2,
[tex]a_2=4\times (2 )^{2-1}\\\\a_2=4\times 2\\\\a_2=8[/tex]
For n = 3,
[tex]a_3=4\times (2 )^{3-1}\\\\a_3=4\times 4\\\\a_3=16[/tex]
This is required formula.
Therefore, the formula that can be used to find the number of monkeys in the nth generation is [tex]\bold{a_n=4\times 2^{n-1}}[/tex]
Learn more about formula here:
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