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  3. 2 fortunately in a not too distant future dorothy

2 Fortunately in a not too distant future Dorothy Gale arrives in her farmhouse and...

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Algebra

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2 Fortunately in a not too distant future Dorothy Gale arrives in her farmhouse and lands on the Wicked Witch and ends her reign of tyranny Munchkins from far and wide return to their homeland but are required to pursue employment in the Emerald City to pay for the damage inflicted by the Wicked Witch The population of Munchkin Land is now modelled via the equation dp dt a 2 t rp 1 rp 1 1 1 sin 172 N 2 2 Set r 0 056 N 10000 and p 0 10000 and p 0 3000 130 where 8 and 3 are the respective fifth and sixth digits of your student number i e if 8 1 and 3 then r 0 051 and p 0 3130 a Set a 200 and use ode45 to simulate the population over a period of ten years Plot and label the Munchkin population as a function of time b How large a value can a take while ensuring the population of Munchkin Land remains positive Support your answer with example simulations in ONE clearly labelled plot Use the legend command to distinguish different a cases 5 MARKS Please include the MATLAB code used in Question 2 and all labelled plots in your final

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