On the first day of a semester, a film club has 90 members. Each day after

Choice B is correct. It’s given that the film club has $90$ members on the first day of a semester, and $10$ new members join the film club each day after the first day of the semester. This means that after $4$ days, $4\times 10$, or $40$, new members will have joined the club. Adding $40$ members to the original $90$ club members yields $130$ members. Thus, the film club will have $130$ total members $4$ days after the first day of the semester.

Choice A is incorrect. This is the number of members that will have joined the film club $4$ days after the first day of the semester if $100$ new members, not $10$, join the film club each day.

Choice C is incorrect. This is the number of members the film club will have $4$ days after the first day of the semester if $1$ new member, not $10$, joins the film club each day.

Choice D is incorrect. This is the number of members the film club has on the first day of the semester.