If , then the three constants , and can be determined from the three equations
These equations are
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Figure 5.6.8(a) Logistic curve from data
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with (numeric) solution . Hence, the desired logistic curve is
In Figure 5.6.8(a) this solution is graphed in black; the asymptote is graphed in red. The astute reader will note that this problem required no calculus at all. It is strictly an algebraic problem of fitting a curve with three parameters to three pieces of data.