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Q.
The exponential growth can be expressed $ w_{t}=w_{0}e^{rt} $ whereas $e$ denotes
AMUAMU 2013Plant Growth and Development
Solution:
Population growth curve are the mathematical expression of the growth of a population, which are used to predict the growth rate of population from its beginning till its climax stage i.e., stability. These growth curve may be $S$-shaped or sigmoid shape or $J$-shaped. The later $J$-shaped curve is shown by small population and contain two phases e.g., lag phase and exponential phase and is represented by following exponential equation $ \frac{dN}{dt}=rN $ Where, $r$ denote intrinsic rate of natural increases and $N$ is size of population, while $dN/dt$ is rate of change in population size. The integral form of the above reaction can be derived as $ W_{t}=W_{0}\,e^{n} $ where, $ W_{t}= $ population density after time $t$ $ W_{O}= $ population density at time $0$ $e$ = the base of natural logarithm $r =$ intrinsic rate of natural increase.