# 2013F002/A9

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# 1. Activity 1: Generate the Computer Model

Problem Statement: Compute the sum of the positive ODD integers from 1 to 10 and then repeat for 1 to 100; 1 to 1,000; 1 to 10,000; 1 to 100,000 and 1 to 1,000,000

# 2. Activity 2: Generate the Computer Model

Initial news report: The snowshoe hare (Lepus americanus), which weighs 1.4—2.3 kilograms on average and 50% of the time is colored white (the other 50% of the time it’s colored brownish gray), lives freely in the wild in upper North America. There were 150,000 hares present in the Canadian Rocky Mountains at the beginning of May, 2009 (95% of them were colored brownish gray at that time). The entire population increased at a rate of 8.35% per month until the end of December, 2010. From September 2010 through the end of December 2010, the Canadian Rockies experienced greater than average snowfall, which was beneficial to the survival of the hares due to their white coloration at that time. How many snowshoe hares were present in the Canadian Rockies at the end of July, 2010?

Extracted Science Model: There were 150,000 hares present at the beginning of May, 2009. The entire population increased at a rate of 8.35% per month until the end of December, 2010. How many snowshoe hares were present at the end of July, 2010?

Initial population: 150,000 Rate of growth: 8.35% per month Growth period: 14 months

Math Model: dP/dt=0.0835*P (continuous model) P(0)=150,000

P(t+∆t)=P(t)+∆t*0.0835*P(t) (discrete model) P(1)=150000.00

# 3. Activity 3: Generate the Computer Model

Initial news report: When considering whether or not to invest, the 13-week US Government Treasury Bill interest rate is an important benchmark to use for comparison purposes. This rate, called the “risk free rate” is the interest underlying almost all other financial instruments. The US Government’s 21 July 2011 T-bill auction established the 13-week T-bill interest rate at 0.02%. Your bank, on the other hand, offers a certificate of deposit (CD) that pays a monthly interest rate of 0.0175%; funds deposited into the CD may not be accessed prior to its annual redemption date. The London Inter-Bank Offered Rate (LIBOR) was 0.18725% as of 21 July 2011. Assuming that your bank CD can be purchased today, what is its final value upon redemption?

Extracted Science Model: Your bank offers a certificate of deposit (CD) that pays a monthly interest rate of 0.0175%; funds deposited into the CD may not be accessed prior to its annual redemption date. Assuming that your bank CD can be purchased today, what is its final value upon redemption?

Initial deposit: \$10,000 Rate of growth: 0.0175% per month Growth period: 1 year

Math Model: dP/dt=0.000175*P (continuous model) P(0)=10,000

P(t+∆t)=P(t)+∆t*0.000175*P(t) (discrete model) P(1)=10000.00

# 4. Activity 4: Generate the Computer Model

Extracted Science Model: “A population of rabbits on an island reproduces at a rate of 50% per year, but 2% die each year due to predation by foxes. There are initially 100 rabbits on the island and 20 foxes. Foxes die of natural causes at a rate of 20% per year, but the fox population grows by 0.1% per year due to “interactions with rabbits.” How many rabbits and foxes will be on the island forty years later?”

Math Model:

R(t+∆t)=R(t)+0.50*R(t)-0.02*R(t)*F(t) (rabbit population) R(1)=100

F(t+∆t)=F(t)-0.20*F(t)+0.001*R(t)*F(t) (fox population) F(1)=20

# 5. Activity 5: Generate the Computer Model

Extracted Science Model: There’s a gaze of 50 raccoons living in the forests of northern Minnesota on 1 January of year 1. These raccoons reproduce at a rate of 12.5% per year. However, whenever their population exceeds 80, a, deadly disease instantly kills 90% of them. How many raccoons are living in the forests of northern Minnesota on 1 January of year 35?

# 6. Activity 6: Generate the Computer Model

Extracted Science Model: A cornfield contains a total of 1000 bushels of corn on April 1. Each month that it’s sunny, the corn’s growth rate is 15% for that month. In every cloudy month, however, the corn’s growth rate drops to 5%. If this particular cornfield experiences 75% chance of a sunny month from 1 April through 1 October, how many bushels of corn will we likely harvest from it on 2 October?

Random Numbers: The following command generates a random number from 0.0 to 1.0 and stores teh value in the variable "chance_of_sun". So if you wanted to set A=1, 60% of the time and A=2, 40% of the time over ten years

for i=[1:10]
chance_of_sun=rand
if (chance_of_sun <= 0.6)
A=1
else
A=2
end
end


Now write the program for the science model.