The whole family has been sucked into a math POW (problem of the week) that has been vexing Miriam. We have tried solving the problem in 27 different ways, using color-coded charts, excel spreadsheets, algebraic formulae, playing with fibonacci numbers -- you name it, we've tried it. We always arrive at the same answer. You'd think that would suggest convincingly that we've done it right. But no. Miriam's teacher insists that answer is wrong. Grrr.
Here's the problem:
Two rats, one male and one female, scampered on board a ship that was anchored at a local dock. The ship set sail across the ocean. When it anchored at a deserted island in late December, the two rats abandoned the ship to make their home on the island. Under these ideal conditions, it might be interesting to estimate the number of offspring produced from this pair in one year. You should make these four assumptions:
- The number of young produced in every litter is six, and three of those six are females.
- The original female gives birth to six young on January 1 and produces another litter of six 40 days later and every 40 days thereafter as long as she lives.
- Each female born on the island will produce her first litter 120 days after her birth and then produce a new litter every 40 days thereafter.
- The rats are on an island with no natural enemies and plenty of food so no rats will die in this first year.
We'd love any assistance on this one. Remember to show your work.