Question 15

15. On Murky Island there is a bear population of 400. Every year, 12% of the bear population dies. Each spring an average of 56 bear cubs are born.

a)determine the bear pop ulation over the next 5 years. Show your work.

year 0 - 400 bears x 88% survival rate(12% mortality rate) + 56 bears born year 1 - 408

year 2 - 415

year 3 - 421

year4 - 426

year5 - 431

b) What will the bear population be after it stabilizes?

The bear population will be at 465, conservatively when it stabilzes.

c) Construct a population graph of the sequence extending the x-axis to include the first 50 years. Lbel the graph.

d) Devise a plan to stabilize the bear population between 400 and 450 bears (inclusive) by the 50 th year using the following parameters:

-he intial bear population is 400

-he birth rate remains at 56 bear cubs per year

the death rate remains at 12% of the population each year

you must cath and transport bears off the island each year

you must stop recreational fishing which results in an increase of up to a maximum of 10 more bears each year.

State the stblized bear population. Show your work to explain how you arrived at your answer.

400 bears x 88% survival rate + 56 bears born + 10 due to fishing restrictions - 16 bears are transported off the island = (400*.88+50).

The stabilized bear population would be at about 415 animals using this formula (400*.88+50)