A research analyst performs database searches for a variety of clients. According to her log, a new search requires approximately 57.0 minutes. Repeated requests on the same or similar topic take less and less time, as her log shows:

Use the following table for calculation. Learning curve coefficients

How many additional searches will it take until the search time gets down to 12 minutes? (Base your calculation on an 'average' learning rate rounded to the nearest percent. Do not round intermediate calculations. Round your 'n' up to the next whole number. Enter your final answer as a whole number.)

\begin{tabular}{lcccccccc} Request no. & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Time (min.) & 57.0 & 40.3 & 38.7 & 28.6 & 28.0 & 27.4 & 27.1 & 19.8 \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow[b]{2}{*}{\begin{tabular}{l} Unit \\ Number \end{tabular}} & \multicolumn{2}{|c|}{70%} & \multicolumn{2}{|c|}{75%} & \multicolumn{2}{|c|}{80%} & \multicolumn{2}{|c|}{85%} & \multicolumn{2}{|c|}{90%} \\ \hline & \begin{tabular}{l} Unit \\ Time \end{tabular} & Total & Unit & Total & \begin{tabular}{l} Unit \\ Time \end{tabular} & Total & Unit & Total & Unit & Total \\ \hline 1 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 \\ \hline 2 & 0.700 & 1.700 & 0.750 & 1.750 & 0.800 & 1.800 & 0.850 & 1.850 & 0.900 & 1.900 \\ \hline 3 & 0.568 & 2.268 & 0.634 & 2.384 & 0.702 & 2.502 & 0.773 & 2.623 & 0.846 & 2.746 \\ \hline 4 & 0.490 & 2.758 & 0.562 & 2.946 & 0.640 & 3.142 & 0.723 & 3.345 & 0.810 & 3.556 \\ \hline 5 & 0.437 & 3.195 & 0.513 & 3.459 & 0.596 & 3.738 & 0.686 & 4.031 & 0.783 & 4.339 \\ \hline 6 & 0.398 & 3.593 & 0.475 & 3.934 & 0.562 & 4.299 & 0.657 & 4.688 & 0.762 & 5.101 \\ \hline 7 & 0.367 & 3.960 & 0.446 & 4.380 & 0.534 & 4.834 & 0.634 & 5.322 & 0.744 & 5.845 \\ \hline 8 & 0.343 & 4.303 & 0.422 & 4.802 & 0.512 & 5.346 & 0.614 & 5.936 & 0.729 & 6.574 \\ \hline 9 & 0.323 & 4.626 & 0.402 & 5.204 & 0.493 & 5.839 & 0.597 & 6.533 & 0.716 & 7.290 \\ \hline 10 & 0.306 & 4.932 & 0.385 & 5.589 & 0.477 & 6.315 & 0.583 & 7.116 & 0.705 & 7.994 \\ \hline 11 & 0.291 & 5.223 & 0.370 & 5.958 & 0.462 & 6.777 & 0.570 & 7.686 & 0.695 & 8.689 \\ \hline 12 & 0.278 & 5.501 & 0.357 & 6.315 & 0.449 & 7.227 & 0.558 & 8.244 & 0.685 & 9.374 \\ \hline 13 & 0.267 & 5.769 & 0.345 & 6.660 & 0.438 & 7.665 & 0.548 & 8.792 & 0.677 & 10.052 \\ \hline 14 & 0.257 & 6.026 & 0.334 & 6.994 & 0.428 & 8.092 & 0.539 & 9.331 & 0.670 & 10.721 \\ \hline 15 & 0.248 & 6.274 & 0.325 & 7.319 & 0.418 & 8.511 & 0.530 & 9.861 & 0.663 & 11.384 \\ \hline 16 & 0.240 & 6.514 & 0.316 & 7.635 & 0.410 & 8.920 & 0.522 & 10.383 & 0.656 & 12.040 \\ \hline 17 & 0.233 & 6.747 & 0.309 & 7.944 & 0.402 & 9.322 & 0.515 & 10.898 & 0.650 & 12.690 \\ \hline 18 & 0.226 & 6.973 & 0.301 & 8.245 & 0.394 & 9.716 & 0.508 & 11.405 & 0.644 & 13.334 \\ \hline 19 & 0.220 & 7.192 & 0.295 & 8.540 & 0.388 & 10.104 & 0.501 & 11.907 & 0.639 & 13.974 \\ \hline 20 & 0.214 & 7.407 & 0.288 & 8.828 & 0.381 & 10.485 & 0.495 & 12.402 & 0.634 & 14.608 \\ \hline 21 & 0.209 & 7.615 & 0.283 & 9.111 & 0.375 & 10.860 & 0.490 & 12.892 & 0.630 & 15.237 \\ \hline 22 & 0.204 & 7.819 & 0.277 & 9.388 & 0.370 & 11.230 & 0.484 & 13.376 & 0.625 & 15.862 \\ \hline 23 & 0.199 & 8.018 & 0.272 & 9.660 & 0.364 & 11.594 & 0.479 & 13.856 & 0.621 & 16.483 \\ \hline 24 & 0.195 & 8.213 & 0.267 & 9.928 & 0.359 & 11.954 & 0.475 & 14.331 & 0.617 & 17.100 \\ \hline 25 & 0.191 & 8.404 & 0.263 & 10.191 & 0.355 & 12.309 & 0.470 & 14.801 & 0.613 & 17.713 \\ \hline 26 & 0.187 & 8.591 & 0.259 & 10.449 & 0.350 & 12.659 & 0.466 & 15.267 & 0.609 & 18.323 \\ \hline 27 & 0.183 & 8.774 & 0.255 & 10.704 & 0.346 & 13.005 & 0.462 & 15.728 & 0.606 & 18.929 \\ \hline 28 & 0.180 & 8.954 & 0.251 & 10.955 & 0.342 & 13.347 & 0.458 & 16.186 & 0.603 & 19.531 \\ \hline 29 & 0.177 & 9.131 & 0.247 & 11.202 & 0.338 & 13.685 & 0.454 & 16.640 & 0.599 & 20.131 \\ \hline 30 & 0.174 & 9.305 & 0.244 & 11.446 & 0.335 & 14.020 & 0.450 & 17.091 & 0.596 & 20.727 \\ \hline \end{tabular} Number of additional searches