Final answer:
The rate of change in this situation is $15 per month.
Step-by-step explanation:
The situation can be represented by the equation y = 45 + 15x, where y represents the total cost and x represents the number of months. In this equation, the y-intercept is 45, which represents the one-time fee.
The slope of the equation is 15, which represents the monthly membership charge. For each additional month, the total cost increases by $15.
Therefore, the rate of change in this situation is $15 per month.