The population of a town is growing according to the differential equation y = ky dt The growth constant, k, is equal to 0.13 year -1. The size of the population at the start of the year 2000 was 5 thousand. Since the population is growing exponentially, the population in year t is given by y = 50.13t 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 2009? (Enter your answer correct to one decimal place.) Population: * thousand. b. How many years does it take for the population to double? (Enter your answer correct to two decimal places.) Doubling time : * 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 : X thousand. An isotope of a radioactive element has half-life equal to 4 thousand years. Imagine a sample that is so old that most of its radioactive atoms have decayed, leaving just 4 percent of the initial quantity of the isotope remaining. How old is the sample? Give your answer in thousands of years, correct to one decimal place. Age : * thousand years. In this question, you wil estimate the area under the curve from x - 3 to x . 5 using three different Riemann sums. how wil subdivide the interval [3.5) into four sub-intervals of equal witch. The birth rate in a certain city is described by the following function b (t) = 8.48 - 0.04t The city's death rate is given by d (t) = 4 +0.03t2 First subinterval Second lubinterval ! Here, t is measured in years, and t = 0 corresponds to the start of the year 1990. Thiand Reinterval The birth and death rates are measured in thousands of births or deaths per year. fourth subinterval ! At the start of 1990, the population of the city is 300 thousand. Complete the following tating Enter all the following answers correct to two decimal places. a. Calculate the total number of births between the start of 1990 and the end of 1999. Number of births = thousand. b. Calculate the total number of deaths over the same peric Areas (/ ()) + / (2) + 1 (ra) + / (x.) jar Number of deaths = thousand. c. What is the pop tion of the city at the start of year 2000? Population : thousand. d. Considering just the period from the start of 1990 to the start of 2000, over what interval is the population increas (Enter your dates as years, not the number of years since 1990.) Increasing from until Over what interval is the population decreasing? Decreasing from Area ~ { (zi) + 1 (32) + / (za) + f (ra) )Ar until Calculate the area between the curves y = b (! ) and y = d ( f ) for f between 0 and 10. Complete the following table Area : Area ~ {/ (21) + / (x2) + / (z.) + / (rojAr You can castofon the exact ares under the curve wang Area = Ar'dr = F(5) - F(3) where F (1) is an and orfestive of the function / (x) = dir Find an caliderivative of the function / (4). Enter your coos Now find the exact value of the area under the curve. leatice that your value of c does med and should notion that the left end-point calculate