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.

Name: 42. In the African Savanna, lions and cheetahs compete for their gaze
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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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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