1. Use a graph to show an example of a situation where the instantaneous rate of change of the function cannot be determined at a point. Year Years since 1901 0 5 10 15 20 25 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 30 35 40 45 50 55 60 65 70 75 80 85 90 Canadian Population (estimated) 5371 000 6 097 000 7207 000 8 001 000 8 788 000 9 451 000 10 377 000 10 950 000 11 507 000 12 292 000 14 009 000 16 081 000 18 238 000 20 015 000 21 961 999 23 449 791 24 820 393 26 101 155 28 031 394 29 610 757 31 021 251 32 623 490 95 100 105 d) Describe properties of the graph and relate its properties to what you have learned in this unit. e) Determine the equation of a function that could be used to model Canada's population. f) Use the data to estimate the average growth rate for a 5 year period. g) Predict the population of Canada in 2020. What assumptions do you need to make? h) Use your equation from e) to estimate the population of Canada in 1973. i) Determine the rate at which the population of Canada is increasing in 1911. j) Determine the rate at which the population of Canada is increasing in 1996. k) How long will it take Canada to reach a population of 50, 000, 000? 1) Rewrite your equation in part d) using base 'e'. m) Rewrite your derivative equation using base 'e'. n) Sketch the derivative of the function. Discuss the properties of the derivative function in relation to the original function. 1. Use a graph to show an example of a situation where the instantaneous rate of change of the function cannot be determined at a point. Year Years since 1901 0 5 10 15 20 25 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 30 35 40 45 50 55 60 65 70 75 80 85 90 Canadian Population (estimated) 5371 000 6 097 000 7207 000 8 001 000 8 788 000 9 451 000 10 377 000 10 950 000 11 507 000 12 292 000 14 009 000 16 081 000 18 238 000 20 015 000 21 961 999 23 449 791 24 820 393 26 101 155 28 031 394 29 610 757 31 021 251 32 623 490 95 100 105 d) Describe properties of the graph and relate its properties to what you have learned in this unit. e) Determine the equation of a function that could be used to model Canada's population. f) Use the data to estimate the average growth rate for a 5 year period. g) Predict the population of Canada in 2020. What assumptions do you need to make? h) Use your equation from e) to estimate the population of Canada in 1973. i) Determine the rate at which the population of Canada is increasing in 1911. j) Determine the rate at which the population of Canada is increasing in 1996. k) How long will it take Canada to reach a population of 50, 000, 000? 1) Rewrite your equation in part d) using base 'e'. m) Rewrite your derivative equation using base 'e'. n) Sketch the derivative of the function. Discuss the properties of the derivative function in relation to the original function