1. Identify the Variables: - Let [tex]\( x \)[/tex] represent the number of months for which the membership is held. - Let [tex]\( y \)[/tex] represent the total cost of the membership after [tex]\( x \)[/tex] months.
2. Define the Costs: - The signing fee is a one-time cost of [tex]$100.
- The monthly fee is $[/tex]30 per month.
3. Formulate the Function Rule: To calculate the total cost [tex]\( y \)[/tex] for [tex]\( x \)[/tex] months, we need to add the initial signing fee to the total cost of [tex]\( x \)[/tex] months of membership fees.
So, the function rule is: [tex]\[
y = 100 + 30x
\][/tex]
4. Calculate the Total Cost After 2 Years: - There are 12 months in a year. - After 2 years, the total number of months ( [tex]\( x \)[/tex] ) is [tex]\( 2 \times 12 = 24 \)[/tex] months.
Using our function rule [tex]\( y = 100 + 30x \)[/tex], we substitute [tex]\( x = 24 \)[/tex]:
[tex]\[
y = 100 + 30 \times 24
\][/tex] [tex]\[
y = 100 + 720
\][/tex] [tex]\[
y = 820
\][/tex]
Therefore, after 2 years, you've spent a total of $820 on the gym membership.
