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Chap3_Sec7_Biology

Chap3_Sec7_Biology - BIOLOGY Example 6 Let n = f(t be the...

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Let n = f ( t ) be the number of individuals in an animal or plant population at time t . square4 The change in the population size between the times t = t 1 and t = t 2 is n = f ( t 2 ) – f ( t 1 ) BIOLOGY Example 6

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AVERAGE RATE So, the average rate of growth during the time period t 1 t t 2 is: 2 1 2 1 ( ) ( ) average rate of growth f t f t n t t t - Δ = = Δ -
The instantaneous rate of growth is obtained from this average rate of growth by letting the time period t approach 0: 0 growth rate lim t n dn t dt Δ → Δ = = Δ Example 6 INSTANTANEOUS RATE

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Strictly speaking, this is not quite accurate. square4 This is because the actual graph of a population function n = f ( t ) would be a step function that is discontinuous whenever a birth or death occurs and, therefore, not differentiable. BIOLOGY Example 6
However, for a large animal or plant population, we can replace the graph by a smooth approximating curve. BIOLOGY Example 6

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To be more specific, consider a population of bacteria in a homogeneous nutrient medium.
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