# Population dynamics of the Tribble

Many people know the Tribble(a hairy puffball) from STAR TREK, my teacher has a tribble on her desk and she warned me not to feed it. I didn’t know why so I searched it up on the internet. You shouldn’t feed a tribble because of its ridiculous rate of reproduction every 12 hours the tribble gives birth to 10 more for a total of 11 Tribbles every 12 hours. $f(x)=11^x$

I calculated how many generations of Tribbles it would take to make a ball of Tribbles as big as the earth. First I used the volume of the earth: $1.08321×10^1^2&space;km^3$ and the volume of a tribble: $268cm^3$. Then I divided them and got how many Tribbles it would need to fill up the earth, taking the log base 11 is how many tribble generations it would need for 1 Tribble to make a sphere of Tribbles as big as the earth.

The next day I talked to my calculus teacher Mrs.Morrison about it, she suggested for me to search up Exponential growth and Logistic growth which are both often used in modelling population size. Exponential growth is what you get if you have a population that has no constraints, Logistic growth is the result of a limited resource like food or space.

The tribble function is an example of exponential growth but if there was limited food it would be best modelled by logistic growth.

It would take 32 generations or 16 days for one tribble to produce a sphere of Tribbles as big as the Earth.

Links below are some of the resources I used to write this post:

CARE AND FEEDING OF THE PET TRIBBLE

MIT introductory biology

Exponential & logistic growth KHAN ACADEMY

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