1. Find a function f given that the slope of the tangent line to the graph of f at any point P(x, y) is given by y' = − 4xy x2 + 1 and the graph of f passes through the point (2, 1).
2. The world population at the beginning of 1980 (t = 0) was 4.5 billion. Assuming that the population continued to grow at the rate of approximately 2%/year, find a function Q(t) that expresses the world population (in billions) as a function of time t (in years since 1980).
What will be the world population at the beginning of 2012? (Round your answer to one decimal place.)
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