

1. 
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. 
20 
B. 
49 


C. 
46 
D. 
25 


Hint 


2. 
Find the first four iterates of the function f(x) = x^{3} if the initial value is x_{0} = 1. 


A. 
1, 1, 1, 1 
B. 
1, 1, 1, 1 


C. 
1, 1, 1, 1 
D. 
1, 1, 1, 1 


Hint 


3. 
If you put $2500 in a savings account with a 7% annual yield, how much money will be in the account after 5 years if you leave it untouched? 


A. 
$3,506.38 
B. 
$13,375 


C. 
$35,496.43 
D. 
$2,675 


Hint 


4. 
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. 
72 
B. 
81 


C. 
79 
D. 
83 


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 

