The spring quail population in a national forest depends on the amount of feed placed throughout the forest during the preceding winter. A spring census finds that the population is $f(x) = \frac{2x+3}{x+2}$ in thousands of individuals when the feed is $x$ in hundreds of kg. • Plot $f(x)$ and $f'(x)$. • Find the average rate of change of the spring quail population between the feed 400 kg and 600 kg and give an interpretation. • Find the rate of change of the spring quail population when the feed is 400 kg.
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Let's choose some values for x, such as 0, 1, 2, and 3. When x = 0, f(0) = 0 + 2 = 2 and f(0+1) = 1 + 2 = 3 When x = 1, f(1) = 1 + 2 = 3 and f(1+1) = 2 + 2 = 4 When x = 2, f(2) = 2 + 2 = 4 and f(2+1) = 3 + 2 = 5 When x = 3, f(3) = 3 + 2 = 5 and f(3+1) = 4 + 2 = Show more…
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