Exponential Equation: num. of rats after 1 year of breeding

eulB

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Jan 20, 2005
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Weve been learning about exponential equations in class (Imp 3). We were asigned a POW (problem of th week) about rats:

A male and female rat get stuck on an island in late Decemer. She gives birth on January 1st to a litter of 6, and will continue to give birth every 40 days. Every litter will always have six pups: three males and three females. Each female (the daughter rats) will produce a liter 120 days after birth, and will continue to reproduce every 40 days.

Find the number of rats after one year (the following January 1st), including the orginal pair.

I attempted to draw out the situation, but stopped after 7 rows or generations because I was so confused. I know you can do this with an equation or a graph....i think. Can anyone help?
 
Day 1- 2
Day 40- 8
Day 80 -14
Day 120 - 20
Day 160 - 26?
Day 200 - 44?

It makes me confused id like to make an equation but i just cant figure out the veriables or an equation idk...im a MORON! Roar
 
eulB said:
Day 1- 2
Day 40- 8
Day 80 -14
Day 120 - 20
Day 160 - 26?
Day 200 - 44?
Try working with the unsimplified numbers, to see if you can find a pattern.

. . . . .Day 0: 1 male, 1 female (total: 2)
. . . . .Day 40: 1+3 = 4 males, 1+3=4 females (total: 8)
. . . . .Day 80: 1+3+3 = 7 males, 1+3+3 = 7 females (total: 14)

After this point, the offspring start getting in on the game, so you might want to make a table with columns or something.

. . . . .Day 120: 7 males to start with, plus the alpha female
. . . . .has three more, plus the first litter of females each have
. . . . .three more, for 7 + 3 + 3(3) = 19 males.
. . . . .7 females to start with, plus the alpha female has three
. . . . .more, plus the first litter of females each have three
. . . . .more, for 7 + 3 + 3(3) = 19 females. (total: 38)

From now on, each additional forty days (each step in the computations) will bring another "level" of females into play. See if you can figure out a formula from this. (The links provide some assistance, by the way.)

eulB said:
It makes me confused id like to make an equation but i just cant figure out the veriables or an equation idk...im a MORON! Roar
I'm sorry, but I don't know what this means.

Eliz.
 
Thanks i was drawing pictures of rats

Roar means im angry

and

A moron is me
 
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