Exponential Population Growth exam Flashcards
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Terms in this set (29)
Exponential Population Growth
A model describing how populations grow exponentially when the per capita growth rate (r) is positive and constant.
What is the equation for exponential population growth?
nt = n0 * e(rt)
Per Capita Growth Rate (r)
The rate at which the population grows per individual, assumed to be constant in the exponential growth model.
What does 'nt' represent in the exponential growth equation?
The final population size.
Euler's Number (e)
A mathematical constant approximately equal to 2.71828, used in the exponential growth equation.
What shape does the exponential growth curve typically have?
A J-shaped curve.
Why is exponential population growth unsustainable in nature?
Because resources are limited, preventing populations from growing exponentially forever.
What is the significance of the 'r max' value?
It is the maximum per capita population growth rate, species-specific, and occurs under ideal conditions.
What happens to the exponential growth curve if 'r' is increased?
The population size increases faster, making the curve steeper.
dN/dt = rN
An equation describing the instantaneous population growth rate at any time instant.
What does 'dN/dt' represent?
The slope of the line tangent to any single point on the exponential growth curve.
What does 'N0' represent in the exponential growth equation?
The initial population size.
ΔN/Δt = rΔt * N
An equation describing the average population growth rate over a discrete time interval.
What does 'rΔt' represent?
The apparent per capita population growth rate in a specific time interval.
What is the relationship between population size and growth rate in exponential growth?
The growth rate is directly proportional to the population size.
What does the slope of the tangent line on the exponential growth curve indicate?
The instantaneous population growth rate at that point.
What is the effect of a smaller 'r' value on the exponential growth curve?
The population grows slower, resulting in a less steep curve.
What does 't' represent in the exponential growth equation?
The elapsed time.
What is the shape of the exponential growth curve when 'r' is 1.0?
A J-shaped curve.
What does the equation ΔN/Δt describe?
The slope of the line connecting any two points on the exponential growth curve.
What is the intrinsic rate of increase?
Another term for the per capita population growth rate (r).
What is the significance of the constant 'e' in the exponential growth equation?
It ensures the growth is exponential, representing continuous growth.
What does the exponential growth model assume about 'r'?
That 'r' is always positive and constant.
What is the relationship between 'r' and the speed of population growth?
The greater the value of 'r', the faster the population size will increase.
What does the equation nt = n0 * e(rt) describe?
The exponential growth curve of a population.
What is the effect of limited resources on exponential population growth?
It inhibits populations from growing exponentially forever.
What does the term 'apparent per capita population growth rate' refer to?
The growth rate over a specific time interval, denoted as rΔt.
What is the shape of the exponential growth curve when 'r' is 0.5?
A less steep J-shaped curve.
What does the equation dN/dt = rN describe?
The instantaneous population growth rate at any time instant.