Lect11 - Exponential Growth Consider an organism with continuous birth and deaths(i.e bacteria in the gut generations overlap Instead of measuring

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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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Population size ( N ) d N dt Population size ( N ) d N 1 dt N r Populations growing exponentially also exhibit the following characteristics: 1) positive feedback of population size on population growth: larger populations grow faster than do smaller populations 2) per capita population growth is constant population growth rate vs. population size per capita population growth rate vs. population size Remember: d N /d t = rN
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N t = N 0 e rt 2N 0 = N 0 e rt ln (2 N 0 /N 0 ) = rt ln(2) = rt t d = ln(2)/r ~ 0.69/r Doubling time: bacteria = 20 min
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This note was uploaded on 05/23/2008 for the course OCHEM 112b taught by Professor Shoeller during the Spring '08 term at UC Riverside.

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Lect11 - Exponential Growth Consider an organism with continuous birth and deaths(i.e bacteria in the gut generations overlap Instead of measuring

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