Notes = = = population growth rate Example 1: There are 300 falcons living in a certain forest at the beginning of 2013. Suppose that every year there are 50 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. so 30 = rmax 300 so rmax = .10 The falcon population will increase by 10% each year. c. Fill in the 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 Interpret the value. We have two data points: (2013, 300) and (2018, 483). Average rate of change = slope falcons/year. Over the past five years, the falcon population has increased by 36.6 per year on average. Example 2: had a population of 49,000 in the year 2013. The infrastructure of the city allows for a carrying capacity of 60,000 people. rmax = .9 for . a. Is the current population 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)? = 8085 people/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:
Notes = = = population growth rate Example 1: There are 300 falcons living in a certain forest at the beginning of 2013. Suppose that every year there are 50 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. so 30 = rmax 300 so rmax = .10 The falcon population will increase by 10% each year. c. Fill in the 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 Interpret the value. We have two data points: (2013, 300) and (2018, 483). Average rate of change = slope falcons/year. Over the past five years, the falcon population has increased by 36.6 per year on average. Example 2: had a population of 49,000 in the year 2013. The infrastructure of the city allows for a carrying capacity of 60,000 people. rmax = .9 for . a. Is the current population 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)? = 8085 people/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:
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