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To help save an endangered species like the cheetah, you must start by understanding its behavior. Only the brave need apply for this job, however, because this kind of biological study is up close and personal. Featured: Susan Millard, Research Supervisor, Center For Reproduction Of Endangered Species, Zoological Society of San Diego.  

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Variables

• Population size

• Rate of reproduction (number of new cheetahs born each year in comparison to the total cheetah population)

• Rate of attrition (number of cheetahs that die each year in comparison to the total cheetah population)

• Time

Expressions and Equations

• If P is the population at the start of the year, Y is the number of young that are born and survive, and D is the number of cheetahs that die in a year, then the population at the end of the year is given by this expression:

P + Y - D

• If P is the population at the start of the year and Y is the number of young that are born and survive in that year, then the rate of reproduction is given by this expression:

Y/P

• If no animals arrive from the outside of the region being studied, and no animals leave to the outside, then the population at the beginning of one year (say, 1996) is related to the population at the beginning of the next year (say, 1997), by this equation (where R is the rate of reproduction and A is the rate of attrition):

P₁₉₉₇ = P₁₉₉₆ +  P₁₉₉₆ (R - A)

Skill Set: "Population Equations"
Use principles of algebra to rearrange and solve one variable equations.  View standards

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Patterns, Relations and Functions

• The total population, P, is related to the rate of reproduction, R
  

• The total population, P, is related to the rate of attrition, A
  

• The total population, P, is related to the amount of time that passes, t

Linear Equations and Functions

• If one is developing a plan for recovery of an endangered species which start with a population of, say, 200 animals, and projects a growth in population each year of “10 animals”, then the population, P, will be related to the number of years that pass, t, by this equation:

P = 10t + 200

Real-World Problem: "Saving the Bald Eagle"
Develop a plan to recover an endangered species, based on linear and non-linear projections. View standards

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Exponential Equations and Functions

• For a species which is being protected from its natural enemies, the relationship between “Number of young produced” (Y) and “time” (t) can in general be modeled as an exponential function of this form:

Y = A·10^kt

Real-World Problem: "Population Growth"
Determine how well an exponential function describes population growth for five different species. View standards

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