# In 2014 there are 60 falcons born and 30 falcons that

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There are 300 falcons living in a certain forest in 2013. In 2014 there are 60 falcons born and 30 falcons that die. a. What is the population growth rate (include units)? Interpret the value. dN/dt = B – D = 60 – 30 = 30 falcons/year. Each year the falcon population will increase by 30 falcons. b. What is the per capita growth rate of the falcons over a year? Interpret the value. N r dt dN max = so 30 = r max 300 so r max = .10 The falcon population will increase by 10% each year. c. Fill in the table and construct a graph. Year Population 2013 300 2014 330 2015 363 2016 399.3 2017 439.23 2018 483.153 d. Find the average rate of change for the falcon population from 2013 to 2018 (include units). Interpret the value. We have two data points: (2013, 300) and (2018, 483). Average rate of change = slope 6 . 36 2013 2018 300 483 = = Δ Δ = x y slope falcons/year. Over the past five years, the falcon population has increased by 36.6 per year on average.

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Example 2: Kentwood, Michigan had a population of 49,000 in the year 2013. The infrastructure of the city allows for a carrying capacity of 60,000 people. r max = .9 for Kentwood. a. Is the current population above or below the carrying capacity? Will the population increase or decrease in the next year? Current population is below the carrying capacity so we would expect the population to increase. b. What will be the population growth rate for 2013 (include units)? Ο Π Ξ Μ Ν Λ = K N K N r dt dN max = = Ο Π Ξ Μ Ν Λ 000 , 60 000 , 49 000 , 60 ) 000 , 49 )( 9 . 0 ( 8085 people for the year c. What will be the population size at the start of 2014. 49,000 + 8085 = 57,085 people d. Fill in the following table: Year Population size Population growth rate 2013 49,000 8085 2014 57,085 2496.041625 2015 59,581 374.4296457 2016 59,955 40.04611425 2017 59,996 4.034052134 e. What happened to the population size over the years? What happened to the population growth rate over the years? Population size got closer and closer to the carrying capacity of 60,000. Population growth rate got smaller and smaller. f. Explain your answer from part (e) using what you know about carrying capacity. As the population gets closer and closer to the carrying capacity, the resources of the environment start to deplete and the growth rate slows. Limiting factors take over (especially density-dependent ones, space, food, water, shelter, etc) g. Explain your answer from part (e) using the formula: Ο Π Ξ Μ Ν Λ = K N K N r dt dN max Look at this part of the formula: Ο Π Ξ Μ Ν Λ K N K As the size of the population (N) gets closer and closer to the carrying capacity (K), then this part of the formula gets smaller and smaller, thus reducing population growth rate.
Primary Productivity – The rate at which organic materials are stored 6CO 2 + 6H 2 O C 6 H 12 O 6 + 6O 2 One can determine Primary Productivity by measuring dissolved oxygen in the water (as it is hard to measure it in the air) Conversion Factors: 1 ml of O 2 = .536 mg of Carbon assimilated To convert: ppm O 2 = mg O 2 /L mg O 2 /L x 0.698 = ml O 2 /L ml O 2 /L x 0.536 = mg carbon fixed/L Fill in the table and Graph Net and Gross Productivity vs % of light Using your data table, what seems to be the trend as the % of light decreases? WHY?

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