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

Question

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. in progress 0 8 mins 2021-07-22T14:27:33+00:00 1 Answers 0 views 0 ## Answers ( ) 1. 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}