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In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of $80$ units, it takes $100$ cycles for failure. When the load is halved, it takes $10000$ cycles for failure. The load for which the failure will happen in $5000$ cycles is _______.

  1. $40.00$
  2. $46.02$
  3. $60.01$
  4. $92.02$
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