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74. LARGE CROWD – EXPONENTIAL GROWTH One of the threats facing our world is the ever increasing human population. This is a problem because the growth is exponential : not only is the population itself growing, but the rate of growth is also increasing in a proportional way. Using calculus, this can be expressed as follows. dP/dt = kP (the rate of change of population P is proportional to P). This is a differential equation, and is easily solved to give P = P0ekt, where P0 is the initial population, t is the time passed, and k is the growth rate. This differential equation (d.e.) is also used in calculating compound interest, the half life of radioactive materials, and in carbon dating.
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