Answer Happy

11. [0.52/2 Points] This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. DETAILS PREVIOUS ANSWERS SCALCET8 9.4.501.XP.MI.SA. The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 150 billion. (Assume that the difference in birth and death rates is 20 million/year = 0.02 billion/year.) Step 1 Let t = 0 correspond to the year 1990. Step 2 Exercise (a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate. Let P be the population in billions and t be the time in years, where t= 0 corresponds to 1990.) We will use billions for our units and assume that the difference in birth and death rates is 20 million/year, which is 0.02 billion/year. We have 1 dp k = P dt 265✔ 1 1 5.3 265 0.02✔ 0.02 Since we are assuming a carrying capacity of M = 150 units, then dp dt = MY NOTES 265(1- - PRACTICE ANOTHER 150 265P (1-50)

Exercise (b) Use the logistic model to estimate the world population in the year 2000. Compare with the actual population of 6.1 billion. Step 1 Rounding to four decimal places, we have A = Submit Skip (you cannot come back) Exercise (c) Use the logistic model P(t) = Step 1 Click here to begin! Exercise (d) What are your predictions if the carrying capacity is 75 billion? Rounding to four decimal places, we have A = Submit Skip (you cannot come back) Need Help? M-P(0) 15.9811 P(0) 150 1+27.3019e-t/265 to predict the world population in the years 2100 and 2500. Read It x. M-P(0) P(0)