Question

PLEASE HELPPPPPPP! Suppose a population of rabbits triples every 4 months, if you start with 10 rabbits, how many would you have after 2 years?

Answer 1

mmmmm.... give me a minute to remember how to do this

Answer 2

Say you start with \(R\) amount of rabbits. In four months, this amount should triple, so after four months, we have \(R \times 3\) number of rabbits. In another 4 months \(\left(4+4 = 8 \ \text{months total} \right) \), we will have tripled once again, so we now have \( \left(R \times 3\right) \times 3\) number of rabbits. In another 4 months \(\left(4 + 4 + 4 = 12 \ \text{months} \right)\), we will have tripled again, so we will have \( \left(\left(R \times 3\right) \times 3 \right) \times 3 \) rabbits.
This is for 12 months. Hopefully you can see the pattern now. Just replace \(R\) with your initial amount of rabbits.

Answer 3

I know there is an easier way than what I am about to do, but I can't think of it.

Answer 4

Thank you so much @DisplayError you to @sleepyjess :)

Answer 5

You got it now?

Answer 6

That is what I was going to show you, but @displayerror got to it before me ^_^

Answer 7

@sleepyjess could you maybe explain this to me a little better?:) or @DisplayError please

Answer 8

Sure! You start with 10 rabbits, after 4 months you have 10*3 rabbits.

Answer 9

So how many rabbits would that be?

Answer 10

30

Answer 11

Ok, now after 8 months total, we have 30*3 rabbits, which is 90.

Answer 12

You see where this is going, or do you want me to continue?

Answer 13

Okay so i need the total for 2 years. so if 8 months equals 90 i guess i can do 90+90+90= 270 rabbits?

Answer 14

Yep, that would be for 1 year, then 270*3= 1 year 4 months, (270*3)*3=1 year 8 months, 270*3*3*3=2 years

Answer 15

So it would be 7,290 rabbits in 2 years? :)

Answer 16

Yeah, \(10 \times 3^6 = 7,290 \ \text{rabbits}\)

Answer 17

Thank you guys SO much!

Answer 18

Yes, aka a lot of rabbits

Answer 19

Oh, I almost forgot ^_^
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Answer 20

Thanks!!!! @sleepyjess

Answer 21

No problemo! :)