744
Chapter 6 | Applications of Integration
Years since 1950 Population (millions)
Years since 1850
Population (thousands)
0
2,556
0
21.00
10
3,039
10
56.80
20
3,706
20
149.5
30
4,453
30
234.0
40
5,279
Source : http://www.sfgenealogy.com/sf/history/ hgpop.htm.
50
6,083
374. [T] The best-fit exponential curve to the data of the form P ( t ) = ae bt is given by P ( t ) =35.26 e 0.06407 t . Use a graphing calculator to graph the data and the exponential curve together. 375. [T] Find and graph the derivative y ′ of your equation. Where is it increasing? What is the meaning of this increase? Is there a value where the increase is maximal? 376. [T] Find and graph the second derivative of your equation. Where is it increasing? What is the meaning of this increase?
60
6,849
Source : http://www.factmonster.com/ipka/ A0762181.html.
370. [T] The best-fit exponential curve to the data of the form P ( t ) = ae bt is given by P ( t ) =2686 e 0.01604 t . Use a graphing calculator to graph the data and the exponential curve together. 371. [T] Find and graph the derivative y ′ of your equation. Where is it increasing and what is the meaning of this increase? 372. [T] Find and graph the second derivative of your equation. Where is it increasing and what is the meaning of this increase? 373. [T] Find the predicted date when the population reaches 10 billion. Using your previous answers about the first and second derivatives, explain why exponential growth is unsuccessful in predicting the future. For the next set of exercises, use the following table, which shows the population of San Francisco during the 19th century.
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