{"id":11292,"date":"2015-07-14T19:33:26","date_gmt":"2015-07-14T19:33:26","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&p=11292"},"modified":"2021-11-08T02:46:00","modified_gmt":"2021-11-08T02:46:00","slug":"solutions-exponential-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-exponential-functions\/","title":{"raw":"Solutions: Exponential Functions","rendered":"Solutions: Exponential Functions"},"content":{"raw":"

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0Linear functions have a constant rate of change. Exponential functions increase based on a percent of the original.\r\n\r\n3.\u00a0exponential; the population decreases by a proportional rate.\r\n\r\n5.\u00a0not exponential; the charge decreases by a constant amount each visit, so the statement represents a linear function.\r\n\r\n7.\u00a0The forest represented by the function [latex]B\\left(t\\right)=82{\\left(1.029\\right)}^{t}[\/latex].\r\n\r\n9.\u00a0After t\u00a0<\/em>= 20 years, forest A will have 43 more trees than forest B.\r\n\r\n11.\u00a0Answers will vary. Sample response: For a number of years, the population of forest A will increasingly exceed forest B, but because forest B actually grows at a faster rate, the population will eventually become larger than forest A and will remain that way as long as the population growth models hold. Some factors that might influence the long-term validity of the exponential growth model are drought, an epidemic that culls the population, and other environmental and biological factors.\r\n\r\n13.\u00a0exponential growth; The growth factor, 1.06, is greater than 1.\r\n\r\n15.\u00a0exponential decay; The decay factor, 0.97, is between 0 and 1.\r\n\r\n17.\u00a0[latex]f\\left(x\\right)=2000{\\left(0.1\\right)}^{x}[\/latex]\r\n\r\n19.\u00a0continuous growth; the growth rate is greater than 0.\r\n\r\n21.\u00a0continuous decay; the growth rate is less than 0.\r\n\r\n23.\u00a0[latex]f\\left(-1\\right)=-4[\/latex]\r\n\r\n25.\u00a0[latex]f\\left(-1\\right)\\approx -0.2707[\/latex]\r\n\r\n27.\u00a0[latex]f\\left(3\\right)\\approx 483.8146[\/latex]\r\n\r\n29. 47,622 fox\r\n\r\n31. 1.39%; $155,368.09\r\n\r\n33.\r\n\"Graph\r\n\r\n35.\u00a0B\r\n\r\n37. A\r\n\r\n39. E\r\n\r\n41. D\r\n\r\n43. C\r\n\r\n45.\u00a0Horizontal asymptote: [latex]h\\left(x\\right)=3[\/latex]; Domain: all real numbers; Range: all real numbers strictly greater than 3.\r\n\"Graph\r\n\r\n47. [latex]g\\left(6\\right)=800+\\frac{1}{3}\\approx 800.3333[\/latex]\r\n\r\n49.\u00a0[latex]h\\left(-7\\right)=-58[\/latex]","rendered":"

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0Linear functions have a constant rate of change. Exponential functions increase based on a percent of the original.<\/p>\n

3.\u00a0exponential; the population decreases by a proportional rate.<\/p>\n

5.\u00a0not exponential; the charge decreases by a constant amount each visit, so the statement represents a linear function.<\/p>\n

7.\u00a0The forest represented by the function [latex]B\\left(t\\right)=82{\\left(1.029\\right)}^{t}[\/latex].<\/p>\n

9.\u00a0After t\u00a0<\/em>= 20 years, forest A will have 43 more trees than forest B.<\/p>\n

11.\u00a0Answers will vary. Sample response: For a number of years, the population of forest A will increasingly exceed forest B, but because forest B actually grows at a faster rate, the population will eventually become larger than forest A and will remain that way as long as the population growth models hold. Some factors that might influence the long-term validity of the exponential growth model are drought, an epidemic that culls the population, and other environmental and biological factors.<\/p>\n

13.\u00a0exponential growth; The growth factor, 1.06, is greater than 1.<\/p>\n

15.\u00a0exponential decay; The decay factor, 0.97, is between 0 and 1.<\/p>\n

17.\u00a0[latex]f\\left(x\\right)=2000{\\left(0.1\\right)}^{x}[\/latex]<\/p>\n

19.\u00a0continuous growth; the growth rate is greater than 0.<\/p>\n

21.\u00a0continuous decay; the growth rate is less than 0.<\/p>\n

23.\u00a0[latex]f\\left(-1\\right)=-4[\/latex]<\/p>\n

25.\u00a0[latex]f\\left(-1\\right)\\approx -0.2707[\/latex]<\/p>\n

27.\u00a0[latex]f\\left(3\\right)\\approx 483.8146[\/latex]<\/p>\n

29. 47,622 fox<\/p>\n

31. 1.39%; $155,368.09<\/p>\n

33.
\n\"Graph<\/p>\n

35.\u00a0B<\/p>\n

37. A<\/p>\n

39. E<\/p>\n

41. D<\/p>\n

43. C<\/p>\n

45.\u00a0Horizontal asymptote: [latex]h\\left(x\\right)=3[\/latex]; Domain: all real numbers; Range: all real numbers strictly greater than 3.
\n\"Graph<\/p>\n

47. [latex]g\\left(6\\right)=800+\\frac{1}{3}\\approx 800.3333[\/latex]<\/p>\n

49.\u00a0[latex]h\\left(-7\\right)=-58[\/latex]<\/p>\n\n\t\t\t

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