Project #43204 - Worksheet 1

Worksheet 1

 

 

 

Instructions:  Calculate the answers for the following questions and answer them below.  Be sure to show your math. If you’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.  Partial credit will be given where appropriate.

 

 

 

1.   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 N0)? Hint:  The Malthusian exponential growth model is Nt = N0 + rN0, where r represents the rate of change in population size.

 

 

 

 

2.   Using the Malthusian exponential growth model from question 1, what will the same deer population size be in another year, at the end of N1.  Hint: N0 is no longer 50. You will need to calculate the new N0 accounting for the number of individuals added last year.

 

 

 

 

3.   What will the population be in 2 years, at the end of N2?

 

 

 

4.   If N0=50 and r=0.2, what will the population size be after 5 time periods?

 

 

 

5.   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 Nt=N0*ert.  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.

 

 

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

 

7.   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.  Using this equation, how many years will it take for the original population of deer (N0=50, r=0.40) to double?

 

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

 

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

 

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

 

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