Question

ou and your friend join a new yoga studio that requires a one-time joining fee and monthly payments. (4.5 pts) a. if your friend stays with this studio for 15 months and pays $645 while you stay for 24 months and pay $852, write a linear function that describes the cost of studio membership, c, in terms of the number of months, m. (2.5 pts) a. what is the cost per month and what is the joining fee? (1 pt) b. determine the maximum number of months one can stay with this gym for $1500.

Answer 1

(a) To write a linear function that describes the cost of studio membership, we can use the point-slope form of the equation of a line:

c - c1 = m - m1

where c1 and m1 are the cost and number of months for one of the data points, and m is the number of months. We can use either of the data points to find the equation, but let's use the data for your friend:

c - 645 = (m - 15)(852 - 645)/(24 - 15)

Simplifying, we get:

c = 90m - 645

(b) The cost per month is the slope of the line, which is 90. The joining fee is the y-intercept of the line, which is -645 (since the cost is negative when m = 0, which represents the joining fee).

(c) To determine the maximum number of months for $1500, we can set the cost equal to $1500 and solve for m:

1500 = 90m - 645

2145 = 90m

m = 23.83

Since we can't stay for a fraction of a month, the maximum number of months we can stay for $1500 is 23 months.