Is it realistic that one female cat would produce 2000 descendants in 18 months? you are given some facts about cats and kittens that will you decide. what is your answer? how can you explain your thinking (or show how you got it)?

variables:
length of pregnancy: about 2 months
age when a female can first get pregnant: about 4 months
number of kittens in a litter: usually 4-6
average number of litters a female cat can have in one year: 3
age when a female cat can no longer have kittens: about 10 years

This is not a realistic idea

Step-by-step explanation:

The most a cat can have in 2 months is typically 6 kittens.

18months / 2 months is 9

So she can have 9 litters in a year, if she's absolutely pumping them out; however, the average number of litters a female can have is 3 litters.

So, let's try 3 x 6 = 18 kittens in a year. Okay, that's much less than 2000.

Let's try the other one then, the 9 time litter.

9 x 6 = 54 Still a lot less than 2000.

If only that one female cat was breeding, there is no way she could make 2000 descendants oh her own within 18 months. If her kittens were added into the equation, it'd be possible, but otherwise, absolutely not.

Yes, this is realistic/possible (albeit not entirely likely, see explanation)

Step-by-step explanation:

Consider the extreme case of a cat always having 6 kittens are they are always all female. Also we start with the original female cat (Call her Alpha) to just about to give birth at month 0 - the beginning of the 18-month count.

From the facts we know that each newly born female kitten can have litter after 6 months, and so do their descendants. A female cat can have second and further litter every 4 months thereafter.

Alpha's first generation is 6 kittens at month 0.  Gen 2, 3, and 4 (their kittens) come at month 6, 12, and 18. The total of new descendant kittens from Alpha's first litter is 6^4=1296.

But Alpha can have next litter at month 4, 8, 12, and 16 (additional to the above). That's 6^3+6^2+6^2 = 344 new descendants and their first litters. The total so far: 1296+344=1640

But Alpha's first generation kittens, can also give additional litter (after the initial 6 months) every 4 months. So that is 6 kittens each can have litter at months 10, 14, 18, each such litter giving rise to the new generations with 6 month period to their first litter. So that is 6 times (6^2+6+6) = 456, thus adding to the total: 1640+456=2096.

So, not counting generations beyond the 1st to "re-litter" we already have more than 2000 kittens! (Who will come up with all the names for them?)

The key assumptions:

- Alpha gives birth right at the beginning of the 18-month count.

- Every kitten born happens to be female (unlikely but possible)

- Every cat maximizes litter production in count and time.

d

step-by-step explanation: