42. In the African Savanna, lions and cheetahs compete for their gazelle. Assume l(t) stands for the population of lions and c(t) stands for the population of cheetahs. In 2015, there were 35,000 lions and 7,000 cheetahs in the Savanna. Assume each pair of lions has six cubs a year, this would mean each lion births three cubs a year, and each pair of cheetahs has two cubs a year. Finally, as each year passes, the number of lions decreases by ½ the number of cheetahs, and the number of cheetahs decreases by ¼ the number of lions. Write equations explaining the rate of change of l(t) and c(t). Solve the IVP (Initial Value Problem) to find general solutions for 1(t) and c(t). Also, find what happens to the ratio of lions to cheetahs at t approaches infinity. Describe each step of your procedure and state your steps clearly. Do not simplify your answer, it is expected that the final answer may be a bit ugly.

42. In the African Savanna, lions and cheetahs compete for their gazelle. Assume l(t) stands for the population of lions and c(t) stands for the population of cheetahs. In 2015, there were 35,000 lions and 7,000 cheetahs in the Savanna. Assume each pair of lions has six cubs a year, this would mean each lion births three cubs a year, and each pair of cheetahs has two cubs a year. Finally, as each year passes, the number of lions decreases by ½ the number of cheetahs, and the number of cheetahs decreases by ¼ the number of lions. Write equations explaining the rate of change of l(t) and c(t). Solve the IVP (Initial Value Problem) to find general solutions for 1(t) and c(t). Also, find what happens to the ratio of lions to cheetahs at t approaches infinity. Describe each step of your procedure and state your steps clearly. Do not simplify your answer, it is expected that the final answer may be a bit ugly.

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Description: 42. In the African Savanna, lions and cheetahs compete for their gazelle. Assume l(t) stands forthe population of lions and c(t) stands for the population of cheetahs. In 2015, there were 35,000lions and 7,000 cheetahs in the Savanna. Assume each pa

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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42. In the African Savanna, lions and cheetahs compete for their gazelle. Assume l(t) stands for
the population of lions and c(t) stands for the population of cheetahs. In 2015, there were 35,000
lions and 7,000 cheetahs in the Savanna. Assume each pair of lions has six cubs a year, this
would mean each lion births three cubs a year, and each pair of cheetahs has two cubs a year.
Finally, as each year passes, the number of lions decreases by ½ the number of cheetahs, and the
number of cheetahs decreases by 4 the number of lions. Write equations explaining the rate of
change of 1(t) and c(t). Solve the IVP (Initial Value Problem) to find general solutions for l(t) and
c(t). Also, find what happens to the ratio of lions to cheetahs at t approaches infinity. Describe
each step of your procedure and state your steps clearly. Do not simplify your answer, it is
expected that the final answer may be a bit ugly.

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