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Biomorph Challenge #1

Tribble Math

From the Biomorph mothership, as it enters our
solar system, this startling message arrives:

"We Biomorphs, the most advanced starfaring beings in the Galaxy, plan to establish an outpost on your planet. Resistance is futile."

"You infinitely insignificant Terrestrial creatures have nothing to say about it, so relax--Biomorphs produce only two offspring per year, so in a hundred years you'll see only two hundred of us.

What do you say?

Flex your math muscles and prepare to meet the Biomorphs!

"The Trouble with Tribbles" © 2006 CBS Studios Inc.

2. Tribbles actually don't age, so they live forever after producing each litter (unless they eat poisoned grain.) With this new assumption:

(a) Uhura brought one tribble onto the Enterprise. Each tribble produced a litter of 10 every 12 hours, calculate how many tribbles there should be in 3 days.

(b) Set up an Excel file to calculate the number of tribbles produced over 5 days. In Excel, plot your results (number of tribbles over time). Print a copy of the plot and the data table.

3. Spock estimates that there would be 1,771,561 tribbles on board (see above question) after 3 days. Which assumption did Spock use?
What actually became of the tribble population on the Enterprise, and why?

4. What is the doubling time of the tribble population?
During the poisoning, the population of tribbles drops to 500 during the poisoning. Assume those tribbles are still producing 10 offspring per litter, but only half survive the poison, and the parent dies after one litter.
What is their new doubling time?

5. In an environment like the Enterprise:
a) How many tribbles would you need initially to produce 1 billion tribbles in 2 days?
b) How many hours would it take for 1 tribble to produce one billion tribbles?

6. In actual natural environments, what phenomena limit the size of growing populations?

7. If there are 1,200,000 tribbles on the Enterprise and Cyrano Jones takes 12 years to pick them up:
a. How many seconds does it take for him to pick up one tribble?
b. Is this answer reasonable? Explain what assumptions you made in finding your answer.
c. How many seconds do you think it would take you to pick up a tribble and stuff it into a bag?
d. Neglecting the time it takes to store the full bags and get empty bags, how many tribbles could you pick up in 12 years? Allow yourself some time to eat and sleep.

** Print all assignments. Handwriting not accepted. **