***These are sub parts of a question, and I've also provided only three of them, as per the policy. Please solve them for me. I only have a few questions left.
1. a)For the following population model (in billions): dP/dt = P − 144P^2
P(0) = 7
Describe the behavior of P(t) as t → +∞?.
b) Initially 100 milligrams of a radioactive substance was present. After 5 hours
the mass had decreased by 4%. If the rate of decay is proportional to the
amount of the substance present at time t, find the amount remaining after
24 hours and also determine the half-life of the radioactive substance.
c) Assume an object weighing 2 lb stretches a spring 6 in. Find the equation of
motion if the spring is released from the equilibrium position with an upward
velocity of 16 ft/sec. What is the period of the motion?.
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