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A cell phone plan costs $39 a month. The plan includes 2 gigabytes (GB) of free data and
charges $15 per gigabyte for any additional data used. The monthly charges are a function of
the number of gigabytes of data used, given by
C (x) = (x)
39, if 0 ⩽ x ⩽ 2
39 + 15 (x − 2), if x > 2
(a) Find C(0.5), C(2), and C(4) .
(b) What do your answers in part (a) represent?
(c) Is C(x) continuous at x = 2?

A cell phone plan costs 39 a month The plan includes 2 gigabytes GB of free data and charges 15 per gigabyte for any additional data used The monthly charges ar class=

Respuesta :

a) The cost of the cell phone plan at x = 0.5, x = 2, and x = 4 are:

C(0.5) = 39,  C(2)  =  39,  C(4)  =  69

b) Answers in part (a) represents the values of C at x = xâ‚€. That is the cost of the cell phone given a certain amount of gigabytes of free data

c) C(x) is continuous at x = 2

Monthly cost of the cell phone C (x) = 39 for 0 ⩽ x ⩽ 2

Since x = 0.5 is in the range 0 ⩽ x ⩽ 2:

C(0.5)  =  39

The monthly charges when given 2 gigabytes of data is $39

Since x = 2 is in the range 0 ⩽ x ⩽ 2

C(2)  =  39

Since x = 4 is in the range x  >  2

C(4) = 39 + 15(x - 2)

C(4) = 39  +  15 (4 - 2)

C(4)  =  39  +  15(2)

C(4)  =  39  +  30

C(4)  =  69

b) The answers in part A represents C(x). That is, the values of C at x = xâ‚€

c) Is C(x) continuous at x = 2

C(2)   =  39

[tex]\lim_{x \to 2} C(x) = 39[/tex]

Since [tex]\lim_{x \to 2} C(x) = C(2)[/tex], the function C(x) is continuous at x = 2

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