how to run increasing number of parallel tasks in bash script

[kirschjoghurt]

1. 
   #!/bin/bash
2. 
   today=$(date +%Y-%m-%d.%H:%M:%S)
3. 
   out_file=res_$today.txt
4. 
   echo 'starting: ' $today > $out_file
6. 
   #will go 1, 10, 20,..., 50
7. 
   for ((b=0, c=1; c <= 50; b++, c=b*10 ))
8. 
   do
9. 
         START=$(date +%s)
10. 
          echo 'tasks: '$c
11. 
          echo 'tasks: '$c >> $out_file
12. 
          for ((a=1; a <= c; a++))
13. 
          do
14. 
                  #run the task in silent mode in background:
15. 
                  sleep 3 > /dev/null 2>&1 &
16. 
          done
17. 
          wait
18. 
          END=$(date +%s)
19. 
          DIFF=$(( $END - $START ))
20. 
          echo "per-task avg execution time (total: $DIFF seconds):" >> $out_file
21. 
          echo $( echo "scale=2;$DIFF/$c" | bc ) >> $out_file
22. 
    done
23. 
    echo 'finished: ' $(date +%Y-%m-%d.%H:%M:%S) >> $out_file