

1. 
Find the first two iterates of the function f(z) = z + 3, if the initial value is 1 + i. 


A. 
7 + i, 10 + i 
B. 
4 + i, 7 + i 


C. 
4i, 7i 
D. 
4 + i, 10 + i 


Hint 


2. 
The Verhulst population model describing the population of antelope in an area is p_{n + 1} = p_{n} + 1.75p_{n}(1  p_{n}). The maximum population sustainable in the area is 60, and the current population is 24. Find the population of the antelope after the first year only. 


A. 
46 
B. 
49 


C. 
20 
D. 
25 


Hint 


3. 
The population of deer in a certain area can be modeled by the Verhulst population model with growth factor 1.5. Presently, there are 68 deer in the area, and a maximum of 80 could possibly be sustained. Find the population of deer after 3 years. (p_{n + 1} = p_{n} + 1.5p_{n} (1  p_{n}) ) 


A. 
83 
B. 
72 


C. 
81 
D. 
79 


Hint 


4. 
Find the first two iterates of the function f (z) = z^{2} + 5, if the initial value is 1  I. 


A. 
2I, 4 


B. 
5  2I, 26  20I 


C. 
35  12I, 1456  960I 


D. 
7, 54 


Hint 


5. 
Find the first three iterates of the function f(z) = z^{2}  8 – 5I if the starting value is 2  i. 


A. 
5  7i, 11i, 7  13i 


B. 
7  5i, 4  5i, 1  5i 


C. 
5 – 9i, 64 + 85i, 3137 – 10885i 


D. 
3  5i, 26  5i, 693  5i 


Hint 

