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Kenneth Rosen Edition 7 Exercise 8.2 Question 34 (Page No. 526)
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Find all solutions of the recurrence relation $a_{n} =7a_{n-1} - 16a_{n-2} + 12a_{n-3} + n4^{n}\:\text{with}\: a_{0} = -2,a_{1} = 0,\:\text{and}\: a_{2} = 5.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 48 (Page No. 526)
Some linear recurrence relations that do not have constant coefficients can be systematically solved. This is the case for recurrence relations of the form $f (n)a_{n} = g(n)a_{n-1} + h(n).$ Exercises $48-50$ ...
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Kenneth Rosen Edition 7 Exercise 8.2 Question 47 (Page No. 526)
A new employee at an exciting new software company starts with a salary of $\$50,000$ and is promised that at the end of each year her salary will be double her salary of the previous year, with an extra increment of $\ ... year of employment. Solve this recurrence relation to find her salary for her $n^{\text{th}}$ year of employment.
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Kenneth Rosen Edition 7 Exercise 8.2 Question 46 (Page No. 526)
Suppose that there are two goats on an island initially.The number of goats on the island doubles every year by natural reproduction, and some goats are either added or removed each year. Construct a recurrence relation for the number of goats on ... assuming that n goats are removed during the $n^{\text{th}}$ year for each $n \geq 3.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 45 (Page No. 526)
Suppose that each pair of a genetically engineered species of rabbits left on an island produces two new pairs of rabbits at the age of $1$ month and six new pairs of rabbits at the age of $2$ months and every month afterward. ... $n$ months after one pair is left on the island.
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