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06 Mar 2025, 22:26
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Dropdown 1: 900
Dropdown 2: 3/2
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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The graph below models the hypothetical population size, in hundreds of individuals, of a local population of Didelphis virginiana for 10 years. Points A, B, and C represent the total population, in hundreds of individuals, at years 3, 5, and 9, respectively, according to the model. The model follows a logistic growth pattern and shows the population as it approaches its carrying capacity, k, of approximately 95,000.
From each dropdown menu, select the option that creates the most accurate statement based on the information provided.
1. For integer values of years from points B to C, the median population size falls at approximately ?
2. Which of the following is closest to the percent increase in population size from year 4 to year 5 as a fraction of the percent increase in population size from year 5 to year 6?
Capture.PNG [ 23 KiB | Viewed 2985 times ]
From each dropdown menu, select the option that creates the most accurate statement based on the information provided.
1. For integer values of years from points B to C, the median population size falls at approximately ?
2. Which of the following is closest to the percent increase in population size from year 4 to year 5 as a fraction of the percent increase in population size from year 5 to year 6?
Attachment:
Capture.PNG [ 23 KiB | Viewed 2985 times ]
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Dropdown 1: 900
Dropdown 2: 3/2
poojaarora1818
Joined: 30 Jul 2019
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Concentration: General Management, Economics
Schools: Duke '26 Haas '26 Kelley '26 Kellogg '26 McDonough '26
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06 Mar 2025, 23:24
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Bismuth83
Solution:
1. For integer values of years from points B to C, the median population size falls at approximately = 600+999/2=900 approx.
2. Which of the following is closest to the percent increase in population size from year 4 to year 5 as a fraction of the percent increase in population size from year 5 to year 6?
Year 4 to 5 = 600-400/400=1/2
Year 5 to 6 = 800-600/600=1/3
So. the fraction of the population from Years 4 to 5 as a fraction population size from year 5 to year 6 is 3/2
08 Mar 2025, 23:00
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1. The population size from years 5 to 9 is increasing, which means the values are already sorted. The median will the value at year 7 or about 90000.
2. The percent increase from year 4 to 5 is equal to \(\frac{Population \ size \ at \ year \ 5 - Population \ size \ at \ year \ 4}{ Population \ size \ at \ year \ 4} * 100\% = \frac{60000 - 40000}{40000} * 100\% = 50\% = \frac{1}{2}\). The percent increase from year 5 to 6 is equal to \(\frac{Population \ size \ at \ year \ 6 - Population \ size \ at \ year \ 5}{ Population \ size \ at \ year \ 5 } * 100\% = \frac{80000 - 60000}{60000} * 100\% = 33.33\% = \frac{1}{3}\). The ratio between the two will be \(\frac{\frac{1}{2}}{\frac{1}{3}} = \frac{3}{2}\).
2. The percent increase from year 4 to 5 is equal to \(\frac{Population \ size \ at \ year \ 5 - Population \ size \ at \ year \ 4}{ Population \ size \ at \ year \ 4} * 100\% = \frac{60000 - 40000}{40000} * 100\% = 50\% = \frac{1}{2}\). The percent increase from year 5 to 6 is equal to \(\frac{Population \ size \ at \ year \ 6 - Population \ size \ at \ year \ 5}{ Population \ size \ at \ year \ 5 } * 100\% = \frac{80000 - 60000}{60000} * 100\% = 33.33\% = \frac{1}{3}\). The ratio between the two will be \(\frac{\frac{1}{2}}{\frac{1}{3}} = \frac{3}{2}\).
