Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100,10),(200,20),(300,30). Do not round fractional answers to the nearest integer.

  and

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

To solve this, we first equate and to 0.

So, we have:

Factor out R in

Split

  or

  or  

Factor out W in

Split

or

Solve for R

Make R the subject

When , we have:

Collect like terms

Solve for W

When , we have:

Collect like terms

Solve for R

So, we have:

When , we have:

So, we have:

Hence, the points of equilibrium are:

  and

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents