Question

Determine the family of logistic functions when the value of\(M\)is fixed and the values of\({\rm{y0}}\)and\({\rm{k}}\)varies.

Short answer

In Figure 1, the family of the logistic functions is sketched with various values of \({\rm{y0}}\)and \({\rm{k = 1}}\) is fixed.

Step-by-step solution

The family logistic functions.

The family of logistic functions is given as\(y = \frac{{{y_0}M}}{{{y_0} + \left( {M - {y_0}} \right){e^{ - iM}}}}\).

Substitute\({\rm{M = 10}}\), then the family of logistic functions becomes\(y = \frac{{10{y_0}}}{{{y_0} + \left( {10 - {y_0}} \right){e^{ - 10{\rm{k}}}}}}\).

Use the online graph calculation to obtain the graph.

Use the online graphing calculator and obtain the graph for the family of logistic functions as shown in Figure 1.

In Figure 1, the family of the logistic function is sketched with various values of \({\rm{y0}}\)and \({\rm{k = 1}}\) is fixed.