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Mathinline
body $k(p)={{k}_{50}}+(5-{{k}_{50}})\frac{(1.7-\log p)}{(1.7-\log {{\beta }_{0}})}$
  for p < 50%

                                                                                                                                                     

Mathinline
body $k(p)={{k}_{50}}$
  for p> 50%

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