## Donnie is considering two different DVD rental stores, both of which have a one-time membership fee and a fee per rented DVD. Th

Donnie is considering two different DVD rental stores, both of which have a one-time membership fee and a fee per rented DVD.

The cost for renting DVDs at the first store is shown below:

Number of DVDs rented Cost ($)

1 5.50

2 7.00

3 8.50

The cost for renting DVDs at the second store is modeled by the linear function C = 5 + 2d, where d is the number of DVDs rented and C is the cost.

Compare the rates of change for each function and explain what this means in terms of the context.

## Answers ( )

Answer:⇒Store i charges $4 for one-time membership fee and a fee of $1.50 per rented DVD

⇒Store ii charges $5 for one-time membership fee and a fee of $2 per rented DVD

⇒ Renting a DVD in shop {i} is cheaper than in shop {ii}

Step-by-step explanation:In the first store, the equation for cost can be calculated as;

Find slope using the data set

Number of DVDs rented Cost {$}

1 5.50

2 7.0

3 8.50

m= Δy/Δx

m= 8.50 – 5.50 / 3-1

m= 3/2 = 1.5

Write the equation

m= Δy/Δx

1.5 = y-7/ x-2

1.5 { x-2 } = y-7

1.5 x – 3.0 = y-7

1.5x -3.0 + 7 = y

1.5 x + 4= y

C= 4 + 1.5 d ——where d is the number of DVDs rented

Comparing the two equations that model the cost of renting DVDs

i) C= 4 + 1.5d

ii) C=5 + 2d

⇒Store i charges $4 for one-time membership fee and a fee of $1.50 per rented DVD

⇒Store ii charges $5 for one-time membership fee and a fee of $2 per rented DVD

For example 2 DVDs are rented in both store, you can find the store which is cheaper as;

i) C= 4 + 1.5d = 4+ 1.5*2 = 4 + 3 = $7

ii) C=5 + 2d = 5 + 2 * 2 = 5 + 4 = $9

⇒ Renting a DVD in shop {i} is cheaper than in shop {ii}