$3.$ It happened, we now live in the time of Star Trek $(2050)$ and can use the teleporter to be beamed anywhere we desire to go$.$ The system allows you to be teleported to any point on planet Earth in less than $3$ hours $(3$ hours and $40$ minutes if you carry a pet with you, but beware: there is a $5\%$ probability of genetic blending at destination$).$ It is projected that about $5$ billion humans $($exactly a third of the Earth$$s population in $2050)$ constitutes the total potential market for this invention.

$3\mathrm{.}1.$ By the end of the first year, there are $200$ million new adopters. What does this tell you about the coefficient of innovation $($p$),$ assuming that the process of diffusion follows the pattern of a Bass model? In other words, p $=\_\_\_\_\_?$