(8 marks) Zooplanktons and Shrimps are two of the animals that live in a water stream/river. The Zooplanktons are eaten by Shrimps. Once a year, the population is counted. We count Shrimps in the hundreds (102) and Zooplanktons in the millions (106). - If Shrimps were not present, the Zooplanktons population would rise by 30% each year. We assume each Shrimp kills 500 Zooplanktons annually. In other words, for each 100 Shrimps, the number of Zooplanktons that gets eaten is (0.5)100,000. - The growth of the Shrimps population is restricted by the availability of the Zooplanktons. We assume that on average, for each of 100,000 Zooplanktons, 10=0.1100 baby Shrimps survive to become adult Shrimps each year. - Finally, we need the death rate of the Shrimps population. It is 30%. That is, only 70% of the adult Shrimps this year survive until next year. This explanation leads to a system of difference equations given as: Sn+1=0.7Sn+0.1ZnZn+1=0.5Sn+1.3Zn (a) Explain what the terms in these equations represent, and how they relate to the information you have here about Zooplanktons and Shrimps. (b) Explain the long-term behaviour of the model. (c) What does the model predict? Do you think both Zooplanktons and Shrimps will thrive