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Unformatted text preview: Thermal Destruction Microbial Growth When no nutrients are limiting bacteria grow by binary fission 2 > 4 > 8 > 16 > 32 > 64 > 128 Time for a growth cycle is called the generation time or the doubling time Phases of growth Lag phase adjustment to new conditions Exponential phase logarithmic growth Stationary phase change components Death phase cells begin to die many cultures die exponentially Figure 8.3 N=N o 2 t/t d ( t d =doubling time) If t d is 20 min in 1 hour N=N o 2 60/20 N=N o 2 3 N=8N o If N o =1 then 1>8 and N=7 If N o =1000 then 1000>8000 and N=8000 Growth is exponential Exponential growth Binary fission each cell becomes two each generation doubles the population result is exponential growth N=2 n N is number of cells n is the generations Figure 8.2 Refresher The natural log ( ln ) is a logarithm in which the base is the irrational number e [ ln 1=0 and ln 2 = 0.693] 2 3 =8 2 ? =8 ?=exponent Exponent 3 the logarithm of 8 with base 2 3 = log 2 8 Log 10 10,000 = ? log b x = a means b n = a Exponential growth Example Starting population 1,000 cells Doubling time 20 minutes 10 generations million cells Figure 8.2 How Does N Change with Time? Slope N/ t is steeper as N increases N/ t = kN (k=specific growth rate) dN/dt = kN dN/N = kdt integrate from No>N 1 and t o>t 1 ln N 1 ln N o = k(t 1t o ) ln N 1 =ln N o + k(t 1t o ) For exponential growth ln N versus time is a straight line, i.e., a linear relationship Application of Equation Doubling time (t...
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 Spring '08

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