Your company, Implants$-$R$-$Us$,$ has developed a new surface modification for an implantable biosensor. The modification will reduce protein adsorption while allowing the sensor to communicate with its surroundings. However, when the number of adsorbed proteins exceed $1$ ng$/$cm$^2.($i$.$e$.,$ n$)$ the sensor will no longer function properly. Given the information below, predict whether the new sensor implant will work properly after $2$ days and after $10$ days. If you had to plot the data of n over $($time$)^1/2,$ what would be the shape of the graph? The sensor is tested in a protein concentration solution of $0\mathrm{.}002$ g$/$L$.$ Assume diffusion mass transport. Assume the diffusion coefficient for the proteins is $10^-6$ cm$^2/$sec$.$