The population of a town is growing according to the differential equation dy _ = k dt 5" The growth constant, k, is equal to 0.12 year '1. The size of the population at the start of the year 2000 was 3 thousand. Since the population is growing exponentially, the population in year t is given by . (Lt?! y = 3!\" Here, y is measured in thousands and t is measured in years since 2000. a. What is the population of the town at the start of the year 2006? (Enter your answer correct to one decimal place.) Population: C] X thousand. b. How many years does it take forthe population to double? (Enter your answer correct to two decimal places.) Doubling time : C] years. c. What will be the size of the population after three doubling times have passed? (That is, after three times the correct answer to part b have passed?) (Enter your answer correct to one decimal place.) Population after three doubling times : [j thousand