The argument must be invalid and has following wrong assumptions: The increasing number of enrollments does mean it will be going as it is to next 50 years or will be doubled over next 50 years, The average rent in the town increased does mean that every apartment in town had increased same amount of rent.
The argument states that the college should build a number of new dormitories because college enrollment is growing and can be doubled over next 50 years. If enrollment is growing now does not mean it will be going, as it is, over next 50 years. There are quite much chances that after next few years the enrollment will decrease and if we build the dormitories just for the sake of future inadequate space for students, then there can be an issue of extra space for students as well. The current trend is not enough to indicate the next 50 years enrollments. However, if there is inadequate space for current enrollments and this happens over the past few years then it is reasonable to build as much dormitories as needed by current students.
The argument also indicated the evidence that there is increasing average apartment rent in the town so college should build dormitories. Average rent increment in town does not ever mean the rent increment of every apartment available in town. For example, if there are some luxury apartments that charge $900 for one room and there are other economical apartments as well that charge $350 for one room, so average is being increased by such luxury outliers. So it is not reasonable to build new dormitories by just seeing the average rent increased in town. However, If we have proper data and statistical results about apartment rents in the town then we could be more specific about our decision and can take that decision in the light of facts and figures.
As without any proper facts and statistical analysis, there are no such chances that students will find it difficult to afford off-campus housing. Hence there are also no evidence that increasing rent in town is of every apartment in town or not, and enrollment is growing current years does not mean it will be do so next 50 years as well.