Star Trek fans may remember when the cute, fuzzy Tribbles quickly became trouble on the starship…

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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