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lect11 - Exponential Growth Consider an organism with...

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Exponential Growth : Consider an organism with continuous birth and deaths (i.e., bacteria in the gut): generations overlap Instead of measuring population change on a yearly or generation time scale, we typically measure changes on very small time scales: instantaneous rates of change . As t 0, Δ N/ Δ t dN/dt = (b - d)N = rN r = instantaneous growth rate or intrinsic rate of increase (individuals per individual per unit time) We can integrate dN/dt from time = 0 to time = t: N t = N 0 e rt lnN t = lnN 0 + rt lnN t - lnN 0 = r t R 0 = e rT ; r = ln(R 0 )/T per generation growth rate r < 0 , population is decreasing r = 0, population is stable r > 0 , population is increasing
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A population growing exponentially has a population curve of characteristic shape! Time ln ( N ) J-shaped curve
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