Bacteria Growth

Bacteria Growth In a certain culture of bacteria, the rate of growth is proportional to the number present. If it is found that the number doubles in 4 hours, how long does it take to get the population 8 fold? Solution - The equation of growth of population where the growth depends on the population at that instant is Pt = P0 e^{kt} Here let the equation be f(x) = ae^{kx} Take a = 1 and take k as a variable. Adjust k to get P_t = 2 at time t = 4 for this mark line || to y axis through x = 4 and shift curve by changing k to get intersection of curve and this line at (4, 2) Alternately find k = (1/t) ln(Pt /P0) named k1 Having obtained k find t for y = 8 it is seen to be 12 hours This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com Solution - The equation of growth of population where the growth depends on the population at that instant is Pt = P0 e^{kt} Here let the equation be f(x) = ae^{kx} Take a = 1 and take k as a variable. Adjust k to get P_t = 2 at time t = 4 for this mark line || to y axis through x = 4 and shift curve by changing k to get intersection of curve and this line at (4, 2) Alternately find k = (1/t) ln(Pt /P0) named k1 Having obtained k find t for y = 8 it is seen to be 12 hours Address your queries to vasantbarve@gmail.com Dr Barve, 12 September 2014, Created with GeoGebra