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. Th 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 following logistic formula. 315 1+14-0.23 N= 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 year of the herd's existence (corresponding to dates up to 2032). N 600 500 400 300 200 100 N 600 500 400 300 200 100 D 5 5 10 10 15 15 20 20 25 30 1 25 30 (d) How many buffalo will there eventually be in the herd? 600 500 400 300 200 100 O N N 600 500 400 300 200 100 O 5 10 5 10 15 15 20 20 (b) How many buffalo are in the herd at the beginning of 2002? buffalo (c) When will the number of buffalo first exceed 2007 (Round your answer to the nearest whole number.) 25 25 30 30 t

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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 following logistic formula.
315
N =
1+14e-0.23
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 year of the herd's existence (corresponding to dates up to 2032).
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Transcribed Image Text:tab os lock esc ^ 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 following logistic formula. 315 N = 1+14e-0.23 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 year of the herd's existence (corresponding to dates up to 2032). control ! 1 600 500 400 300 200 100 O FI N 600 500 400 D Q A option N T 300 200 100 5 N 5 2 F2 10 W 10 (d) How many buffalo will there eventually be in the herd? S 15 command w # X 15 3 20 25 80 F3 E 20 (b) How many buffalo are in the herd at the beginning of 2002? buffalo (c) When will the number of buffalo first exceed 200? (Round your answer to the nearest whole number.) D $ 25 4 C 30 R t 30 F de L % 5 N 600 500 400 300 200 V 100 O N 600 500 400 300 200 100 O T G 5 6 5 10 B 10 Y 15 & 7 15 20 ଏସ F7 20 U 25 30 25 * 8 H J DII FB 30 - N M t ( 9 K DD 19 O < I of ) 0 L 4 F10 P command ^. : ¡ I F11 { + [ option = ? 11 I I 40) F12 } 1 delete 1
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(b) How many buffalo are in the herd at the beginning of 2002?
buffalo
(d) How many buffalo will there eventually be in the herd?
buffalo
(c) When will the number of buffalo first exceed 200? (Round your answer to the nearest whole number.)
(e) When is the graph of N, as a function t, concave up?
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When is it concave down?
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O (0, 11.47)
O (-∞0,00)
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O (0,00)
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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.
O First 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.
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Transcribed Image Text:esc 1 O (b) How many buffalo are in the herd at the beginning of 2002? buffalo (d) How many buffalo will there eventually be in the herd? buffalo (c) When will the number of buffalo first exceed 200? (Round your answer to the nearest whole number.) (e) When is the graph of N, as a function t, concave up? O (11.47,00) 0 (0,00) O (0, 2013) O (0, 315) O (0, 11.47) 5 10 15 20 25 30 When is it concave down? O (0, 2013) O (0, 11.47) O (-∞0,00) O (11.47, ∞) O (0,00) ! 1 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. O First 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. Need Help? F1 Q A Read It @ 2 F2 W C Master It #3 80 F3 E D $ 4 099 000 F4 R L % 5 F5 T 5 10 G ^ 6 F6 Y 15 20 & 7 H aa F7 U * 8 I 25 DII F8 30 ( 9 K DD F9 ) 0 O` 0 J F10 I' P (3) F11
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