In addition to research on zebra mussels in general, you are to consider the following series of scenarios. These scenarios each involve a difference equation of the form X"+1 = (1+r-h)Xn +C where X n represents the size of the population at time n, r is the \"reproduction\" rate, I: is the \"harvesting\" rate, and C is a constant that indicates a constant \"restocking\" or \"removal\" amount. (For specic values of r and h this is the same as the model X"+1 = an + A.) Scenario #1 below provides initial values for h, r, and C and asks you to nd the equilibrium value L for the population. You are then asked to manipulate h and/or C in order to increase or reduce the equilibrium value to a specied value (r is xed). This can be accomplished through \"guess and check\" or by solving for h or C algebraically. You will choose one scenario as a \"best\" scenario and then nd the solution for the difference equation that represents that scenario. Scenario #1: Suppose the zebra mussel population around a particular plant is currently at 3000 cm2. (Since zebra mussels are relatively small creatures, we'll measure their population by the size of the area they inhabit.) Suppose also that the zebra mussel population has a 30% growth rate, that the company's efforts to reduce their numbers removes 50% of the population, and that 1000 cm2 are added to the population each year from outside sources. Write the difference equation for the zebra mussel population in the n+1" year, Xi\