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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 in 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

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 in 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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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. 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
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? 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. 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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