Question

dominic is signing up for a gym membership with a one - time fee and then a monthly fee to remain a member. the total cost of the gym membership over t months is given by the equation c = 45t + 100. what is the y - intercept of the equation and what is its interpretation in the context of the problem?
answer attempt 1 out of 5
the y - intercept of the function is (square) which represents
the one - time joining fee
the total fees for one year
number of months dominic is a member
the monthly fee to remain a member

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In the given equation $C = 45t+100$, we can compare it with the slope - intercept form (here $y = C$ and $x = t$). So, by comparing $C = 45t + 100$ with $y=mx + b$, we find that the $y$-intercept (the value of $b$) is 100.

Step2: Interpret the $y$-intercept

In the context of the gym membership problem, $t$ represents the number of months and $C$ represents the total cost. When $t = 0$ (which means 0 months of membership, i.e., at the time of signing up), the total cost $C=45(0)+100 = 100$. So this 100 should represent the one - time cost associated with signing up, which is the one - time joining fee.

Answer:

The $y$-intercept of the function is 100 which represents the one - time joining fee.