The function y = 15(x – 2) + 45 can be used to determine the total amount of money spent on a gym membership for x months. What is the rate of change of the total amount spent in dollars with respect to the number of months of gym membership?
[This first step isn't entirely necessary.] Using the distributive property, the equation/function y = 15(x-2)+45 simplifies to y=15x+15. Therefore, the rate of change you're looking for is...
15.
extra credit: which 15 represents the rate of change?
To find the rate of change of the total amount spent in dollars with respect to the number of months of the gym membership, we need to take the derivative of the given function with respect to x.
The given function is y = 15(x – 2) + 45, where y represents the total amount spent on a gym membership for x months.
To find the derivative, we apply the power rule and constant multiple rule of differentiation.
Taking the derivative of the function y = 15(x – 2) + 45:
dy/dx = 15(d/dx(x - 2)) + d/dx(45)
The derivative of (x - 2) with respect to x is 1, and the derivative of a constant, 45, is 0.
So, dy/dx = 15(1) + 0 = 15
The derivative of the given function is 15. Therefore, the rate of change of the total amount spent in dollars with respect to the number of months of the gym membership is 15 dollars per month.