In January 2005, the population of California was 36.8 million and growing at an annual rate of 1.3%. Assume that growth continues at the same rate. (a) By how much will the population increase between 2005 and 2035? million (to the nearest 0.001 million) By (b) By how much will the population increase between 2035 and 2065? By million (to the nearest 0.001 million) (c) Explain how you can tell before doing the calculations which of the two answers in parts (a) and (b) is larger. Select ALL statements in A-F which are true if more than one is possible. A. The calculation in part (b) is larger since the exponential function is concave up, and the average rate of change is increasing as time goes on. B. The calculation in part (a) is larger since the function is exponential, and exponential graphs grow faster at first, and then flatten. C. The 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. OD. The two answers are equal since the change in time from 2005 to 2035 is the same as the change in time from 2035 to 2065. Therefore the change in outputs will be the same. E. The calculation in nart (b) is larger since both increases are over 30 year periods, but since the graph of the function bends unward, the increase in the later time period is
In January 2005, the population of California was 36.8 million and growing at an annual rate of 1.3%. Assume that growth continues at the same rate. (a) By how much will the population increase between 2005 and 2035? million (to the nearest 0.001 million) By (b) By how much will the population increase between 2035 and 2065? By million (to the nearest 0.001 million) (c) Explain how you can tell before doing the calculations which of the two answers in parts (a) and (b) is larger. Select ALL statements in A-F which are true if more than one is possible. A. The calculation in part (b) is larger since the exponential function is concave up, and the average rate of change is increasing as time goes on. B. The calculation in part (a) is larger since the function is exponential, and exponential graphs grow faster at first, and then flatten. C. The 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. OD. The two answers are equal since the change in time from 2005 to 2035 is the same as the change in time from 2035 to 2065. Therefore the change in outputs will be the same. E. The calculation in nart (b) is larger since both increases are over 30 year periods, but since the graph of the function bends unward, the increase in the later time period is
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 62SE: Rachael deposits $1500 into a retirement fund each year. The fund earns 8.2% annual interest,...
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Transcribed Image Text:In January 2005, the population of California was 36.8 million and growing at an annual rate of 1.3%. Assume that growth continues at the same
rate.
(a) By how much will the population increase between 2005 and 2035?
By
million (to the nearest 0.001 million)
(b) By how much will the population increase between 2035 and 2065?
By
million (to the nearest 0.001 million)
(c) Explain how you can tell before doing the calculations which of the two answers in parts (a) and (b) is larger. Select ALL statements in A-F
which are true if more than one is possible.
A. The calculation in part (b) is larger since the exponential function is concave up, and the average rate of change is increasing as time goes on.
B. The calculation in part (a) is larger since the function is exponential, and exponential graphs grow faster at first, and then flatten.
C. The 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.
OD. The two answers are equal since the change in time from 2005 to 2035 is the same as the change time from 2035 to 2065. Therefore the change in outputs will be the
same.
OE. The calculation in part (b) is larger since both increases are over 30 year periods, but since the graph of the function bends upward, the increase in the later time period is
larger.
OF. None of the above
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