RecycledCDs, Incorporated, offers a choice of 5 used CDs for $23, With each additional CD costing $7. Write a cost function for purchasing 5 or more CDs. What will the cost of buying 12 CDs be? Let x represent the number of CDs over 5.

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2020-09-19T12:53:01+02:00

Answer:

[tex]C(n)= 7n - 12[/tex] -- Cost Function

Cost of buying 12CDs is $72

Step-by-step explanation:

Given

[tex]Base\ Amount = \$23[/tex]

[tex]Additional\ CD\ Amount = \$7[/tex]

Solving (a): Cost Function

Let n represent CDs greater than 5

[tex]Cost Function = Base Amount + Additional\ CD\ Amount * (n - 5)[/tex]

Substitute:

[tex]Base\ Amount = \$23[/tex] and [tex]Additional\ CD\ Amount = \$7[/tex]

[tex]Cost\ Function = 23 + 7 * (n - 5)[/tex]

[tex]Cost\ Function = 23 + 7(n - 5)[/tex]

Open Bracket

[tex]Cost\ Function = 23 + 7n - 35[/tex]

Collect Like Terms

[tex]Cost\ Function = 7n - 35 + 23[/tex]

[tex]Cost\ Function = 7n -12[/tex]

[tex]C(n)= 7n - 12[/tex]

Solving (b): When n = 12

Substitute 12 for n in [tex]C(n)= 7n - 12[/tex]

[tex]C(12) = 7 * 12 -12[/tex]

[tex]C(12) = 84 - 12[/tex]

[tex]C(12) = 72[/tex]

Cost of buying 12 CDs is $72