The population of snakes at a wildlife park over the course of six months is modeled by the equation y = x5 − 5x4 + 2x3 − 10x2 + 100x + 5, where x is the number of months. if the park officials count 505 snakes, how many months have passed since the initial count was taken?

You are already given an equation where y stands for the population of snakes and x is for the number of months. Since you are given a population of y = 505, you substitute this to equation and find x. A technique is to use the 'shift-solve' feature of a scientific calculator to directly determine the value of x:

505 = x5 − 5x4 + 2x3 − 10x2 + 100x + 5
x = 5 months

This must be true because it is within the specified time bracket of 6 months.