Final answer:
The function that represents the number of students at the college in x years, considering a 13% annual increase and a current student population of 496, is an exponential growth function, N(x) = 496(1.13)^x.
Step-by-step explanation:
The function that best represents the number of students at this college in x years, given that the current number of students is 496 and the number of students increases by approximately 13% each year, is an exponential growth function. The formula for this function is:
N(x) = N_0 (1 + r)^x
Where N(x) is the number of students after x years, N_0 is the initial number of students, r is the rate of increase (expressed as a decimal), and x is the number of years.
Substituting the given values:
N(x) = 496 (1 + 0.13)^x
This function will allow us to calculate the projected enrollment at this college for any given number of years into the future.