1. Use the Gompertz law of mortality to graduate the crude mortality rates obtained from a mortality investigation shown below. Hence check the degree of smoothness of the graduated rates (8marks) Age (x) (Exposed) Ex (no. of deaths) dx 30 70000 39 31 66672 43 32 68375 34 33 65420 31 34 61779 23 35 66091 50 2. The sales of a particular insurance cover satisfy the following logistic growth equation, where initial sales are of 250000. How much are the sales when they are growing the fastest ds 9 dt 1m s(20m-s) (3marks) 3. What should be the annual growth rate if one wants to double one's money in seven years? (2marks) 4. Verify the formula gupen in the tables for the mean of the Parets distribution. For what walues of the parameters is this formula walid? (4marks) 5. The table below shows deaths in thousands from air pollution YEAR POPULATION YEAR POPULATION YEAR POPULATION 1908 1098 1924 706 1940 528 1912 740 1928 510 1944 639 1916 714 1932 278 1948 523 1920 615 1936 448 a) Using the model: P(n+1)=a*P(n)exp(-6*P(n)) obtain the positive constants a and busing the least squares method. P(n) is parent population and P(n+1) is surmining offspring(8marks) 6) Obtain the equilibria populations(5marks) 1. Use the Gompertz law of mortality to graduate the crude mortality rates obtained from a mortality investigation shown below. Hence check the degree of smoothness of the graduated rates (8marks) Age (x) (Exposed) Ex (no. of deaths) dx 30 70000 39 31 66672 43 32 68375 34 33 65420 31 34 61779 23 35 66091 50 2. The sales of a particular insurance cover satisfy the following logistic growth equation, where initial sales are of 250000. How much are the sales when they are growing the fastest ds 9 dt 1m s(20m-s) (3marks) 3. What should be the annual growth rate if one wants to double one's money in seven years? (2marks) 4. Verify the formula gupen in the tables for the mean of the Parets distribution. For what walues of the parameters is this formula walid? (4marks) 5. The table below shows deaths in thousands from air pollution YEAR POPULATION YEAR POPULATION YEAR POPULATION 1908 1098 1924 706 1940 528 1912 740 1928 510 1944 639 1916 714 1932 278 1948 523 1920 615 1936 448 a) Using the model: P(n+1)=a*P(n)exp(-6*P(n)) obtain the positive constants a and busing the least squares method. P(n) is parent population and P(n+1) is surmining offspring(8marks) 6) Obtain the equilibria populations(5marks)