Math  2     Name:_________________________________  Answer  Key  for  Quiz  4A  Review     February  2015   Practice Problems

1. a. f(n) = 13n – 4 𝑓 𝑛 = −4 𝑛 = 0𝑓 𝑛 − 1 + 13 𝑛 > 0

b. f(n) = –11.5n + 49 𝑓 𝑛 = 49 𝑛 = 0𝑓 𝑛 − 1 − 11.5 𝑛 > 0

c. f(n) = 4 * 5n 𝑓 𝑛 = 4 𝑛 = 0𝑓 𝑛 − 1 ∗ 5 𝑛 > 0

d. f(n) = –3n + 8 𝑓 𝑛 = 8 𝑛 = 0𝑓 𝑛 − 1 − 3 𝑛 > 0

2. a. f(n) = 3n2 – n + 5 b. f(n) = –2n2 – 4n + 3 3. a. not a polynomial, no constant differences

b. quadratic, second order constant differences c. exponential, constant ratios

4. d(n) = n2 + 2n

5. a(n) = –4n + 12 𝑎 𝑛 = 12 𝑛 = 0𝑎 𝑛 − 1 − 4 𝑛 > 0

6. b(n) = n2 + 2n – 3 𝑏 𝑛 = −3 𝑛 = 0𝑏 𝑛 − 1 + 2𝑛 + 3 𝑛 > 0

7. c(n) = 2n3 + 1

8. d(n) = 5 * 2n 𝑑 𝑛 = 5 𝑛 = 0𝑑 𝑛 − 1 ∗ 2 𝑛 > 0

9. g(n) = –3 * 4n 𝑔 𝑛 = −3 𝑛 = 0𝑔 𝑛 − 1 ∗ 4 𝑛 > 0

Input, n Output, d(n) Δ=2n+1 Δ2

0 0 3 2

1 3 5 2

2 8 7 2

3 15 9 2

4 24 11 2

5 35 13

6 48