5. The population: P, otan island, yyears after colonization is given by the function P: $. at. What was the initial population of the island? {2 marks} b. How long did it take before the island had a population of "150? (2 marks) c. After how many years was the population growing the fastest? {3 marks} d. Using curve sketching methods: sketch the graph ofthe function. Make sure that you include all steps: charts: and derivations details. {10 marks] e. Give a possible explanation for the shape of the curve