Assignment:
Question 1. The jabby bird is in danger of being placed on the endangered species list, as there are only 975 of the birds known to be in existence. A bird is placed on the list when the known population reaches 100. If 27% of the jabby bird population either dies or is taken by a poacher each year and only 5 new jabby birds are born, write a recurrence relation and initial conditions describing the number jn of jabby birds at the end of n years.
Question 2. Zebra mussels are fresh water mollusks that attack underwater structures. Suppose that the volume of mussels in a confined area grows at a rate of 0.2% per day.
(a) If there are now 10 cubic feet of mussels in a lock on the Illinois River at Peoria, Illinois, develop a recurrence relation and initial conditions that represent the volume mn of the mussel colony n days hence.
(b) Develop a formula expressing mn as a function of n.
Question 3. Find an explicit formula for sn if so,s1,s2,... is a sequence satisfying the given recurrence relation and initial conditions.
Question: sn = sn-1 - 10, so = 32
Question 4. sn = 9sn-2 , so = 1, s1 = 9
Question 5. Suppose that a corporate executive deposits $2000 per year for 35 years into an individual retirement account. If interest is compounded annually at the rate of 8%, how much will the account be worth after the last deposit?
Question 6. If the expression is a polynomial, then compute it completely; otherwise compute it through the x7 term.
A= 1 + x + x2
C= 1 - x2 + x4
Question 7. Give a generating function for the sequence {ar}, and then write it in the form ao + a1x+a2x2+a3x3 + ... through the x6 term.
Question 8. Let ar be the number of ways of choosing r jellybeans from a basket containing 3 licorice, 4 strawberry, and 2 lemon jellybeans.
Question 9. Let ar be the number of ways of spending r dollars on posters, if four identical $1 and three identical $2 posters are available.
Provide complete and step by step solution for the question and show calculations and use formulas.