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 _______.
- $40.00$
- $46.02$
- $60.01$
- $92.02$