Please show all work for full credit! When performing calculations, round number
ID: 2889429 • Letter: P
Question
Please show all work for full credit!
When performing calculations, round numbers to 3 decimal places
1. The California Condor (Gymnogyps californianus) is a critically endangered species. In 1991, 48 adults individuals were released in the wild from the captive breeding program. In 2016, there were approximately 323 individuals in existence.
a. Calculate r for this time frame, assuming a continuous and constant growth rate (2 pts).
b. What is the doubling time of this population (2 pts)?
2. 30 rabbits are introduced onto a small island at the beginning of 2000.
a. If this population has an annual exponential growth rate (lambda) of 1.18 on the island, what was the population size at the beginning of 2010 (2 pt)? Assume discrete growth
b. At the beginning of 2017 (2 pt)?
3. The black-footed ferret (Mustela nigripes) may be downgraded to threatened status (from endangered) once it reaches a total population size of 1300 animals in the wild. If this population has been growing exponentially since 1991 at r = 0.02, calculate when it would be downgraded to threatened status, given a population of 300 animals in the wild in 2015 (2 pt). Assume continuous growth.
Explanation / Answer
multiple questions posted.please post each question seperately
1)
general exponential growth model: A(t)=(A(0))ert
(a)
in 1991, t=0, A(0)= 48
in 2016, t =2016-1991 =25 ,A(25) = 323
A(25)=(A(0))er*25
=>323= 48*e25r
=>e25r =(323/48)
=>25r =ln(323/48)
=>r =(1/25)*ln(323/48)
=>r =(1/25)*ln(323/48) exactly
=>r =0.07625805249259062444777553308023
=>r =0.076 approximately
=>r =7.626% approximately
b)
A(t)=48et(1/25)*ln(323/48)
population doubles.
=>A(t)=2*(A(0))
=>48et(1/25)*ln(323/48) =2*48
=>et(1/25)*ln(323/48) =2
=>t*(1/25)*ln(323/48) =ln(2)
=>t=25*ln(2)/ln(323/48)
=>t=9.0894949176323745068365859694527
doubling time is 9.089 years approximaely
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