University of California, Los Angeles

• LIFESCIENC 30B

• Homework 4 Solutions Feb 9, 2018 Solutions: 5.1.2: Choose an initial value for X and use values of r that are less than, greater than, and equal to one to test the above statements by computing two values of X for each value of r. Solution: Choose X0 = 1, r = 1: X1 = 1 ∗ 1 = 1, X2 = 1 ∗ X1 = 1 ∗ 1 = 1. r = 2: X1 = 2 ∗ 1 = 2, X2 = 2 ∗ 2 = 4. r = 1/2: X1 = 1 2 ∗ 1 = 1 2 , X2 = 1 2 1 2 = 1 4 . 5.1.3: An inedible alga is growing on a pond in a city park. Only a small part of the pond is now covered by the algae, but the area covered is doubling each day. The city decides to remove the algae once it covers half the pond. If the pond will be completely overgrown in thirty days, on what day will it be half covered? (Hint: Try working backward.) Solution: The pond will be completely overgrown in thirty days. Since the algae doubles each day the pond will be half overgrown with algae on the twenty ninth day. On the twenty eighth day it will be less than half covered. So the city will remove the algae on the twenty ninth day. 5.1.4: A rabbit population is growing at 10% a year. If there are 10 rabbits this year and time is discrete, how many will there be in 10 years? Use a loop in SageMath to check your answer. Solution: In this case r = 1.1 and X0 = 10. So X10 = (1.1)10 ∗ 10 = 25.937424601. (Round one way or the other to get the actual rabbit population.) Sage code: init = 10 r = 1.1 for i in range(0,10): x = r*init init = x ini