Question

Based on mark/recapture studies between 2001 and 2006, the Southern Beaufort Sea 2006 population of polar bears is approximately 1526 bears. Suppose that since 2006 the population is being renewed at a rate of

r(t) = 0.180 + 0.012t thousand bears per year

and that the survival rate is 89%, where t = 0 corresponds to 2006.†

(a) How many of the 2006 population of 1526 polar bears will still be alive 27 years from then? (Round your answer to the nearest integer.)
bears

(b) Write a function for the number of polar bears that will be born t years from 2006 and will still be alive 27 years from then.
f(t) =

(c) Estimate the Southern Beaufort Sea population of bears in 2033. (Round your answer to the nearest integer.)
bears

Answer 1

Based on markrecapture studies between 2001 and 2006, the Southern Beaufort Sea 2006 population of polar bears is approximately 1526 bears. Suppose that since 2006 the population is being renewed at a rate of r(t) 0.180 0.012t thousand bears per year and that the survival rate is 89%, where 0 corresponds to 2006t (a) How many of the 2006 population of 1526 polar bears will still be alive 27 years from then? (Round your answer to the nearest integer.) bears P(t) 1526 1550 1432 P(t) 435 439 15 17 18 451 997 457 797 21 472 551 493 461 480 23 24 25 26 498 507 517 10 435 14 432 (b) Write a function for the number of polar bears that will be born t years from 2006 and will still be alive 27 years from then. tt) = P辻+) +0 'gS t l@ot. I2t J-0.89 f0.89 ( 00 4-2 (0.89 (c) Estimate the Southern Beaufort Sea population of bears in 2033. (Round your answer to the nearest integer.) bears Number beers in 2033 3 526 bears