Consider two population functions P1(t) and P2(t), both of which satisfy the logistic equation with the same limiting population M but with different values k1 and k2 of the constant k in Eq. Assume that k1 < k2. Which population approaches M the most rapidly? You can reason geometrically by examining slope fields (especially if appropriate software is available), symbolically by analyzing the solution given in Eq., or numerically by substituting successive values of t.
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