The ladder reader

You will write three small functions that read a gel with a ladder and count the efficiency of competent cells.

The idea. The log of the size is a straight line against the distance. A least squares line has the slope $\dfrac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}$. The efficiency is the colonies for each microgram of DNA that was on the plate.

Your tasks.

1. Finish fit_line. It takes the distances and the sizes of the ladder, and gives the slope and the intercept of the line of log10 of the size against the distance.
2. Finish size_at. It gives the size of a band from its distance, the slope and the intercept.
3. Finish efficiency. It gives the colonies for each microgram, from the colonies, the nanograms of DNA used and the fraction of the cells that was plated.