Question

Conservationists will take snow geese off the endangered species list when the population hits 10,000. If populations are sustaining growth at r = 0.088 and the population in 2001 is 3000 individuals, in what year will snow geese be taken off the endangered species list?A) between 2106 and 2109B) between 2009 and 2012C) between 2012 and 2015D) between 2015 and 2018

Answer 1

The population of snow geese will increase in the year between 2012 and 2015 so that they can be struck off the endangered species, which means option C is the right answer.

The population of snow geese as a function of the time 't' in years is given by the equation:

Growth rate = r = 0.088 (given)

Population in time 't' = P(t) = 3000 * [e^(0.088t)]         ....(1)

t = 0, in 2001

For the snow geese to be taken off the endangered species list, we get the following equation:

P(t) = 10,000         ....(2)

Putting values of equation (2) in equation (1):

10000 = 3000 * [e^(0.088t)]

Taking logarithms both sides, we get;

ln(10000) = ln(3000) + ln[e^(0.088t)]

Solving the equation for 't', we get;

t = 13.6 years

Adding 13.6 to 2001, we get the year 2014.6, which suggests that the population will rise above endangered limit in the year 2014 and 2015.

Learn more about snow geese at:

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