lim 2- 818 . lim 40(1-4) #100 5. lim a when a > 1 n(n+1) 7....

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lim 2- 818 . lim 40(1-4) #100 5. lim a" when a > 1 n(n+1) 7. lim 4-1²-1 √n - n+1 9. lim find the limits. 11. 13. 2'4' 6'8' 10 12345 2'5' 10' 17' 26 2. lim 3" 818 N₁+1 = N₁ + 2 #x1+2- lim a" when 0 <a<1 10 4. lim 6. 8. lim In Problems 11-14, write a, explicitly as a function of n on the basis of the first five terms of the sequence a,, n = 0, 1, 2,..... 13579 2 6 12 20 30 24 8 16 32 1234 3'4'5'6 12. 14. 0. 10. lim n² + n-6 n-2 n+1 15. Saving the Red Wolf You are trying to build a mathemat- ical model for the size of the red wolf population in North Carolina. Red wolves are a critically endangered species, once found throughout the southeastern United States but now found mainly in a single North Carolina wildlife reserve. The data in this question come from U.S. Fish and Wildlife Service (2007). (a) If the population size r years after the start of a study on red wolf numbers is N,, start by writing a word equation so that N₁41 can be predicted from N₁: number of pups born in one year number of wolves that die We will derive the formula of each of the terms in the word equation. (i) It is possible to count the number of pups born in given year. A subset of these data is given in the following table: Year N₁ Number of Pups Born 1990 18 1993 44 1996 70 1999 126 2002 123 2005 115 3 16 16 37 33 41 Plot the number of pups against the population size N₁. Show that the data are consistent with the following formula for the number of pups born in one year: Number of pups born in one year= -0.28N, [Hint: Draw the line given by this equation on your data plot.] (ii) Independently conservationists are measuring the number of red wolf deaths in each year. Red wolves are killed by hunters. and ranchers, or by being struck by vehicles. The conservation- ists estimate that in one year 22% of red wolves are killed. Write recurrence relation for the population size N₁. 98 (iii) Assuming that the current population size is No = 130 wolves, use your formula from (ii) to predict the population size N, for the next 10 years (i.e., calculate N₁, N₂...... N₁0). (iv) The current conservation goal for the wild red wolf popula- tion is to reach 220 individuals. When, according to your model, will that population size be reached? lim 2- 818 . lim 40(1-4) #100 5. lim a" when a > 1 n(n+1) 7. lim 4-1²-1 √n - n+1 9. lim find the limits. 11. 13. 2'4' 6'8' 10 12345 2'5' 10' 17' 26 2. lim 3" 818 N₁+1 = N₁ + 2 #x1+2- lim a" when 0 <a<1 10 4. lim 6. 8. lim In Problems 11-14, write a, explicitly as a function of n on the basis of the first five terms of the sequence a,, n = 0, 1, 2,..... 13579 2 6 12 20 30 24 8 16 32 1234 3'4'5'6 12. 14. 0. 10. lim n² + n-6 n-2 n+1 15. Saving the Red Wolf You are trying to build a mathemat- ical model for the size of the red wolf population in North Carolina. Red wolves are a critically endangered species, once found throughout the southeastern United States but now found mainly in a single North Carolina wildlife reserve. The data in this question come from U.S. Fish and Wildlife Service (2007). (a) If the population size r years after the start of a study on red wolf numbers is N,, start by writing a word equation so that N₁41 can be predicted from N₁: number of pups born in one year number of wolves that die We will derive the formula of each of the terms in the word equation. (i) It is possible to count the number of pups born in given year. A subset of these data is given in the following table: Year N₁ Number of Pups Born 1990 18 1993 44 1996 70 1999 126 2002 123 2005 115 3 16 16 37 33 41 Plot the number of pups against the population size N₁. Show that the data are consistent with the following formula for the number of pups born in one year: Number of pups born in one year= -0.28N, [Hint: Draw the line given by this equation on your data plot.] (ii) Independently conservationists are measuring the number of red wolf deaths in each year. Red wolves are killed by hunters. and ranchers, or by being struck by vehicles. The conservation- ists estimate that in one year 22% of red wolves are killed. Write recurrence relation for the population size N₁. 98 (iii) Assuming that the current population size is No = 130 wolves, use your formula from (ii) to predict the population size N, for the next 10 years (i.e., calculate N₁, N₂...... N₁0). (iv) The current conservation goal for the wild red wolf popula- tion is to reach 220 individuals. When, according to your model, will that population size be reached?

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Certainly Lets go through each of the limit problems in more detail 1 lim 401 4 x as x approaches infinity As x approaches infinity the value of 4x ap... View the full answer