LS 30B MIDTERM SOLUTIONS University of California, Los Angeles LIFESCIENC 30B
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Course
LIFESCIENC 30B
Institution
LIFESCIENC 30B
LS 30B: MATHEMATICS FOR LIFE SCIENTISTS
WINTER 2018 - LECTURE 2
Jukka Keranen
MIDTERM SOLUTIONS
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, 1. (10 pts) Dragons are born from eggs after a long incubation period, and young dragons must fight adult dragons in order
to survive to adulthood themselves. Write down a differential equation model of the adult dragon population (D), by
using the following assumptions.
• Being more fierce and more resilient, females make up 70 per cent of all adult dragons.
• Female dragons lay eggs at a constant per-capita rate r per year, and it takes 10 years for the eggs to hatch.
• It takes 50 years for a newly hatched dragon to grow into an adult.
• When a young dragon is 20 years old, it is abandoned by its mother, and must fight adult dragons for territory. Consequently,
the fraction of young ones that survive this stage in their lives is a decreasing sigmoid function of the adult population.
• Since adult dragons constantly fight one another, the death rate of adult dragons is an increasing sigmoid function of the
adult population, with a maximum per-capita death rate of 10 per cent.
• Being peerless in power and essentially immortal, dragons only die in combat with other dragons.
(Hint. Draw a timeline, starting from when an egg is laid up to when the dragon born from that egg turns into an adult.)
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