**Worksheet 1**

Â

Â

Â

**Instructions:**Â Calculate the answers for the following questions and answer them below.Â Be sure to show your math. If youâ€™d like to do this Worksheet in Excel rather than in Word, you are welcome to do that and attach it instead. Each question is worth 10 points, 5 for the answer itself and 5 for showing/explaining your work.Â Partial credit will be given where appropriate.

Â

Â

Â

1.Â Â Given that a deer population of 50 animals is increasing at a rate *r* of 0.4, how many deer will be added to the population in the first year (at the end of N_{0})? Hint:Â The Malthusian exponential growth model is N_{t} = N_{0} + *r*N_{0}, where *r* represents the rate of change in population size.

Â

Â

Â

Â

2.Â Â Using the Malthusian exponential growth model from question 1, what will the same deer population size be in another year, at the end of N_{1}.Â Hint: N_{0} is no longer 50. You will need to calculate the new N_{0} accounting for the number of individuals added last year.

Â

Â

Â

Â

3.Â Â What will the population be in 2 years, at the end of N_{2}?

Â

Â

Â

4.Â Â If N_{0}=50 and *r*=0.2, what will the population size be after 5 time periods?

Â

Â

Â

5.Â Â You can see if you want to predict N into the far future, using the Malthusian exponential equation will be time consuming. For predicting N into the future, we tend to prefer the continuous growth model where N_{t}=N_{0}*e^{rt}.Â Using this equation, calculate the predicted population size after 5 time periods given that N0=50 and r=-0.2. Hint: e is a mathematical constant.

Â

Â

6.Â Â Given that r=0.023 per year, what will the population size be in 2010 if N0=1370 in 2000?

Â

7.Â Â Recall from the text that the time it takes for a population to double in size is calculated by the following equation: Doubling Time = 0.693/r.Â Using this equation, how many years will it take for the original population of deer (N_{0}=50, *r*=0.40) to double?

Â

8.Â Â A population with an r=-0.2 is decreasing.Â According to the model, will such a population ever reach zero? Is this realistic? Explain your answer.

Â

9.Â Â As a land or wildlife manager, when might these types of population change predictions be useful? Explain your answer.

Â

10.Â Â Â What was the most interesting thing you have learned so far?Â Why is the most interesting to you?

Â

Subject | Mathematics |

Due By (Pacific Time) | 10/12/2014 09:00 am |

Tutor | Rating |
---|---|

pallavi Chat Now! |
out of 1971 reviews More.. |

amosmm Chat Now! |
out of 766 reviews More.. |

PhyzKyd Chat Now! |
out of 1164 reviews More.. |

rajdeep77 Chat Now! |
out of 721 reviews More.. |

sctys Chat Now! |
out of 1600 reviews More.. |

sharadgreen Chat Now! |
out of 770 reviews More.. |

topnotcher Chat Now! |
out of 766 reviews More.. |

XXXIAO Chat Now! |
out of 680 reviews More.. |