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# GROWTH EQUATIONS

GROWTH EQUATIONS. Biot 309 Fall, 2012. Generation Time. N = (log 10 N f – log 10 N o ) / .301 N Number of generations N f Final Concentration of Cells N o Original concentration of cells .301 Conversion Factor to Convert Log 2 to Log 10. generation (doubling) time.

## GROWTH EQUATIONS

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1. GROWTH EQUATIONS Biot 309 Fall, 2012

2. Generation Time N = (log10Nf – log10No ) / .301 N Number of generations Nf Final Concentration of Cells No Original concentration of cells .301 Conversion Factor to Convert Log2 to Log10

3. generation (doubling) time

4. What is a Logarithm? • Logarithm is a functionthat gives the exponent in the equation bn = x. It is usually written as logbx = n. • For example: 34 = 81 Therefore log3 81 = 4

5. Example 1N = (log10Nf – log10No ) / .301 Measure Culture at 9:00 a.m. 10,000 cells / ml Measure Culture at 3:00 p.m. 100,000 cells / ml Calculate N N = (log10Nf – log10No ) / .301 N = (5-4)/0.301 N = 1/0.301 N = 3.33 Generations in 6 Hours We Know: 6 Hours = 360 Minutes Therefore: Generation Time = 360 Minutes / 3.33 Generations N = 108 Minutes to Generate

6. Example 2N = (log10Nf – log10No ) / .301 Measure Culture at 9:00 a.m. 10,000 cells / ml Measure Culture at Noon 1,000,000 cells / ml Calculate N

7. Example 2N = (log10Nf – log10No ) / .301 Measure Culture at 9:00 a.m. 10,000 cells / ml Measure Culture at Noon 1,000,000 cells / ml Calculate N N = (log10Nf – log10No ) / .301 N = (6-4)/0.301 N = 2/0.301 N = 6.64 Generations in 3 Hours We Know: 3 Hours = 180 Minutes Therefore: Generation Time = 180 Minutes / 6.64 Generations N = 27 Minutes to Generate

8. Example 3N = (log10Nf – log10No ) / .301 Measure Culture at 9:00 a.m. 2000 cells / ml Measure Culture at 1:00 p.m. 18,000 cells / ml Calculate N

9. Example 3N = (log10Nf – log10No ) / .301 Measure Culture at 9:00 a.m. 2000 cells / ml Measure Culture at 1:00 p.m. 18,000 cells / ml Calculate N N = (log10Nf – log10No ) / .301 N = (4.25-3.30)/0.301 N = .95/0.301 N = 3.16 Generations in 4 Hours We Know: 4 Hours = 240 Minutes Therefore: Generation Time = 240 Minutes / 3.16 Generations N = 75.9 Minutes to Generate N = 1.27 Hours to Generate

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