In January 2005, population of California was 36.8 million and growing at annual rate of 1.3%. Suppose that growth continues at same rate.
(a) By how much will population increase between 2005 and 2030?
(b) By how much will population increase between 2030 and 2055?
(c) Describe how to tell before doing calculations which of two answers in parts (a) and (b) is larger. Choose all statements in A-F which are true if more than one is feasible.
A. Calculation in part (a) is larger since the graph of the function is concave down, and the average rate of change is decreasing as time goes on.
B. Calculation in part (a) is larger since the function is exponential, and exponential graphs grow faster at first, and then flatten.
C. Calculation in part (b) is larger since exponential function is concave up, and average rate of change is increasing as time goes on.
D. Two answers are equal since change in time from 2005 to 2030 is same as change in time from 2030 to 2055. Hence change in outputs will be same.
E. Calculation in part (b) is larger since both increases are over 25 year periods, but as graph of function bends upward, increase in later time period is larger.
F. None of the above.