# Project #43204 - Worksheet 1

Worksheet 1

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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.

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

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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 N1.Â  Hint: N0 is no longer 50. You will need to calculate the new N0 accounting for the number of individuals added last year.

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

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

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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 Nt=N0*ert.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.

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

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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 (N0=50, r=0.40) to double?

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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.

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

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

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