Question

After 6 months, the total cost of Tanya’s gym membership was $200. After 8 months, the total cost was $260. Is this a proportional or non-proportional relationship? Question 11 options: Proportional; the constant of proportionality is $33.33/month Proportional; the constant of proportionality is $32.50/month Non-proportional; the rate of change is $20/month Non-proportional; the rate of change is $30/month

Answer 1

Non-proportional; the rate of change is $30/month

Explanation:

After 6 months, the total cost was $200.

After 8 months, the total cost was $260.

Find the rate of change using formula

`(f(b)-f(a))/(b-a)`

Hence,

`\text{Rate of change}\\ \\=(\$260-\$200)/(8-6)\\ \\=(\$60)/(2)\\ \\=\$30\ \text{per month}`

At this rate, after 6 months Tanya paid

`\$30\cdot 6=\$180`

But after 6 months, the total cost of Tanya’s gym membership was $200.

It means the relationship passes through the point (0,20), not through the origin. Each proportional realtionship passes through the origin. Thus, this is not proportional relationship.