#1 (Mahaffy¹, #10 p. 188) Below are data on the population of a species of moth that inhabits an island and breeds annually (then dies). Suppose the population model has the form Pn = rPn-1 + μ where n is measured in years after 1990. That is, P₁ = population in 1990, P₁ = population in 1991, etc. a) From the data in the table below determine the updating function for this population, i.e., find r and μ. (Hint: Write two equations and solve for r and μ.) Year 1990 1991 1992 Moths 6000 5500 5100 b) Use the model to find the population of moths in 1993, 1994, and 1995.

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#1 (Mahaffy¹, #10 p. 188) Below are data on the population of a species of moth that inhabits an island
and breeds annually (then dies). Suppose the population model has the form
Pn = rPn-1 + μ
where n is measured in years after 1990. That is, P₁ = population in 1990, P₁ = population in 1991,
etc.
a) From the data in the table below determine the updating function for this population, i.e., find r
and μ. (Hint: Write two equations and solve for r and μ.)
Year
1990
1991
1992
Moths
6000
5500
5100
b) Use the model to find the population of moths in 1993, 1994, and 1995.
Transcribed Image Text:#1 (Mahaffy¹, #10 p. 188) Below are data on the population of a species of moth that inhabits an island and breeds annually (then dies). Suppose the population model has the form Pn = rPn-1 + μ where n is measured in years after 1990. That is, P₁ = population in 1990, P₁ = population in 1991, etc. a) From the data in the table below determine the updating function for this population, i.e., find r and μ. (Hint: Write two equations and solve for r and μ.) Year 1990 1991 1992 Moths 6000 5500 5100 b) Use the model to find the population of moths in 1993, 1994, and 1995.
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