ckWaterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo (bison) herd that spends falls and winters in the Park. Theherd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the following logistic formula.315N =1+14e-0.23tHere t is the number of years since the beginning of 2002, the first year the herd is unmanaged.(a) Make a graph of N versus t covering the next 30 year of the herd's existence (corresponding to dates up to 2032).escN6005004003002001100N600500400300200100OBlQ5A5N102F210W15S15(b) How many buffalo are in the herd at the beginning of 2002?21✓buffalow非X20#32080F3E2525D$3044(c) When will the number of buffalo first exceed 200? (Round your answer to the nearest whole number.)14x(d) How many buffalo will there eventually be in the herd?C888F4tR2030tFO%5600500400300200100N6005004003002001000VNFST5G510A6Fó10YB152015 20&7H44F7U25 3025*8J30DIFBtIN M(9KDDF9O)0<IHLF10P.SF11;I|| +{=[?2111mI}1deleteL tabos lockesc21(c) When will the number of buffalo first exceed 200? (Round your answer to the nearest whole number.)14X(d) How many buffalo will there eventually be in the herd?buffalo(e) When is the graph of N, as a function t, concave up?O (11.47,0)0 (0,00)O (0, 2013)(0, 315)O (0, 11.47)XWhen is it concave down?O (0, 2013)● (0, 11.47)✔buffaloO (-00,00)O (11.47, ∞)O (0,0)What does this mean in terms of the growth of the buffalo herd?O First the herd is shrinking at a decreasing rate, then the rate at which the herd shrinks increases.O'First the herd is growing at a decreasing rate, then the rate of growth increases.!Need Help?1First the herd is growing at an increasing rate, then the rate of growth decreases.O First the herd is shrinking at a decreasing rate, then the rate at which the herd shrinks decreases.F1QAxNRead It Master It@2F2WS#3X80F3ED$4C888F4RLLF5FSTA6GF6YB&7H94F7U** 008DIFBI(9J KN MDbF9-00<LF10I'P>:4)F11;+ 11{[4011F12I?I}1delet

# As per the guidelines we are entitled to solve maximum of three subparts at a time, please…

Answered: 100 N 600 500 400 300 200 100 5 5 10 15…

100 N 600 500 400 300 200 100 5 5 10 15 10 15 20 25 20 25 t 30 30 100 N 600 500 400 300 200 100 O 5 15 10 10 15 15 20 20 t 30 25 25 30 t

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.2: Graphs

Problem 25E: Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky...

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Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.
What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
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