The genetics service of a large veterinary hospital gets referrals for three or four male tortoiseshell cats every year. These cats are invariably sterile and have underdeveloped testes. How are these tortoiseshell male cats produced?

The proportion of male tortoiseshell cats is very low. This happens because the colors are linked to sex because they are exclusively on the X chromosome, to have two colors (black and orange) must have two X chromosomes from the father and mother .

For a male cat to be tortoiseshell, a genetic anomaly must occur: the presence of two X chromosomes and one Y (XXY).

This is a perfect example of exponential decay. In this case the growth factor should be represented by a fraction, and it is! This forest, starting out with apparently ( 800? ) pine trees, has a disease spreading, which kills 1 / 4th of each of the pine trees yearly. Therefore, the pine trees remaining should be 3 / 4.

Respectively 3 / 4 should be the growth factor, starting with 800 pine trees - the start value. This can be represented as such,

- where a = start value, b = growth factor, t = time ( variable quantity )

____

Thus, the function can model this problem. The forest after t years should have P( t ) number of pine trees remaining.