1. The population of the world was 5.28 billion in 1990 and 6.07 billion in 2000. Find an exponential model for these data and use the model to predict the world population in the year 2022. (1.5 marks) O 7.25 billion O 7.90 billion O 8.25 billion. O 8.90 billion O None of above2. The population of the world was 5.28 billion in 1990 and 6.07 billion in 2000. Assume that the limiting population is 15 billion. Find an logistic model for these data and use the model to predict the world population in the year 2022. Correct to two decimal places (in billion). [1.5 marks) - _ 7.25billion 7.90 billion ." 8.25billion 8.90billion - _' Noneofabove. 3. A freshly brewed cup of coffee has temperature 95\"C in a 20\"C room. When its temperature is 7D\"C, it is cooling at a rate of 2\"C per minute. When does this occur? Correct the answer to 1 decimal place (in minute). [2 ma rks) . . After 5.1 minutes. After 10.1 minutes. - After 15.2 minutes. - After 20.3 minutes. None ofabove. 5. Consider the following initial value problem :12 d d +20d:+100yzosuchthatyz1andy :lath. Find the value of a: such that y : 0. [1.5 marks) ". None of above. 4. Find the particular solution to the following boundary value problem: dx2 dx d'y dy + 54 = 0, y = 1atx = 0 andy = 2 at x = 1/2. (1.5 marks) O y = e 2 cos x + 2e-2 sin x. O y = e 27 cosx + 2eTe 2 sin x. O y = e " cosx + 2e Te 27 sin x O y = e 27 cos x - 2eTe 2 sin x. O None of above.6. Consider the following initial value problem: day dy _2y = et such that y = 0 and dy da2 dx = 0 at x = 0. da Find the value of dy do.3 atx = 0 (2 marks) O 5 O 6 O 7 O 8 O None of above