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So it is better to say the rate of change (at any instant) is the growth rate times the population at that instant:Īnd that is a Differential Equation, because it has a function N(t) and its derivative.Īnd how powerful mathematics is! That short equation says "the rate of change of the population over time equals the growth rate times the population".ĭifferential Equations can describe how populations change, how heat moves, how springs vibrate, how radioactive material decays and much more. When the population is 2000 we get 2000×0.01 = 20 new rabbits per week, etc. The bigger the population, the more new rabbits we get! When the population is 1000, the rate of change dN dt is then 1000×0.01 = 10 new rabbits per week.īut that is only true at a specific time, and doesn't include that the population is constantly increasing. Let us imagine the growth rate r is 0.01 new rabbits per week for every current rabbit. Think of dN dt as "how much the population changes as time changes, for any moment in time". Then those rabbits grow up and have babies too! The population will grow faster and faster. The more rabbits we have the more baby rabbits we get.
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