User responses cleared Homework:HW SECTION 9.5 Question 8, 9.5.38 Part 4 of 7 HW Score: 91.07%, 7.29 of 8 points Points: 0.29 of 1

Skip to Main content Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question content area top Part 1 A​ nation's population​ (to the nearest​ million) was 281 million in 2000 and 311 in 2010. It is projected that the population in 2050 will be 437 million. To construct a logistic​ model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts​ (a) through​ (f) to use one approach. Question content area bottom Part 1 a. Assume that tequals0 corresponds to 2000 and that the population growth is exponential for the first ten​ years; that​ is, between 2000 and​ 2010, the population is given by Upper P left parenthesis t right parenthesis equals Upper P left parenthesis 0 right parenthesis e Superscript rt. Estimate the growth rate r using this assumption. requals    0.01014 ​(Round to five decimal places as​ needed.) Part 2 b. Write the solution of the logistic equation with the value of r found in part​ (a). Write any populations in the logistic equation in millions of people. ​P(t)equals    StartFraction negative Upper K times 281 Over e Superscript negative 0.01014 t Baseline left parenthesis negative Upper K plus 281 right parenthesis minus 281 EndFraction Part 3 Use the projected value Upper P left parenthesis 50 right parenthesis equals 437 million to find a value of the carrying capacity K. Kequals    2744.39 ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.) Part 4 c. According to the logistic model determined in parts​ (a) and​ (b), when will the​ country's population reach​ 95% carrying​ capacity? The population will reach​ 95% of the carrying capacity in the year    enter your response here. ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.) r(Round to five decimal places as needed.)P(t)K(Type an integer or decimal rounded to the nearest hundredth as needed.)The population will reach 95% of the carrying capacity in the year(Type an integer or decimal rounded to the nearest hundredth as needed.)K(Type an integer or decimal rounded to the nearest hundredth as needed.)K(Type an integer or decimal rounded to the nearest hundredth as needed.)Choose the correct response below.r(Round to five decimal places as needed.)P(t)K(Type an integer or decimal rounded to the nearest hundredth as needed.)The population will reach 95% of the carrying capacity in the year(Type an integer or decimal rounded to the nearest hundredth as needed.)K(Type an integer or decimal rounded to the nearest hundredth as needed.)K(Type an integer or decimal rounded to the nearest hundredth as needed.)Choose the correct response below.r(Round to five decimal places as needed.)P(t)K(Type an integer or decimal rounded to the nearest hundredth as needed.)The population will reach 95% of the carrying capacity in the year(Type an integer or decimal rounded to the nearest hundredth as needed.) Get more help