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.

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Acacia 8 mins 2021-07-22T14:27:33+00:00 1 Answers 0 views 0

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    2021-07-22T14:29:18+00:00

    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}

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