title: Formula with features: unity at zero, zero at inf and control over the shape
body: <p>I would like to seek help in finding a formula for following shape and behavior with controllability over behavior. 
  with following features: y=f(x)</p>
  
  <ol>
  <li>y-> unity (or controllable constant) as x->0 </li>
  <li>y->0 as x->inf </li>
  <li>Steep  fall after x=constant </li>
  <li>Control over the average slope of the steep. for example, slope at y=0.5. (lover  priority)</li>
  <li>Graph y=f(x) would be something like: </li>
  </ol>
  
  <p><img src="https://i.stack.imgur.com/IqJhB.png" alt="enter image description here"></p>
  
  <p>Thanks</p>
  
  <p>SAM</p>