Star Trek fans may remember when the cute, fuzzy Tribbles quickly became trouble on the starship Enterprise. One Tribble was trapped in the ship and a single Tribble actually produces in a litter of 10 Tribbles every 12 h. Mr. Spock claimed that after 3 days, there were already 1,771,561 Tribbles.
(a) Was Spock correct?
(b) Use mathematical modeling to represent the way the Tribble population changes over time as a differential equation.
(c) Solve the differential equation numerically and provide a plot of the Tribble population for a week.
(d) When was the Tribble population 500,000? will the Tribble population reach 4,000,000?
(e) Experiment with your model and incorporate a removal mechanism. At which rate would the Tribbles need to be removed to have them all off the ship in a day?
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