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?
1 answer
Question:
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?
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?
Answers
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) = 69b) Answers in part (a) represents the values of C at x = x₀. That is the cost of the cell phone given a certain amount of gigabytes of free datac) C(x) is continuous at x = 2Monthly cost of the cell phone C (x) = 39 for 0 ⩽ x ⩽ 2Since x = 0.5 is in the range 0 ⩽ x ⩽ 2:C(0.5) = 39The monthly charges when given 2 gigabytes of data is $39Since x = 2 is in the range 0 ⩽ x ⩽ 2C(2) = 39Since x = 4 is in the range x > 2C(4) = 39 + 15(x - 2)C(4) = 39 + 15 (4 - 2)C(4) = 39 + 15(2)C(4) = 39 + 30C(4) = 69b) The answers in part A represents C(x). That is, the values of C at x = x₀c) Is C(x) continuous at x = 2C(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 = 2Learn more here: https://brainly.com/question/20710468
Similar Solved Questions
1 answer
PROBLEM 6. 10 A histogram has mean 70 and standard deviation 5 If the histogram is not bell shaped but it is symmetric. Find the least proportion of data falls between 70 and 80 If the histogram is bell shaped. Find the proportion of data between 65 and 77
PROBLEM 6. 10 A histogram has mean 70 and standard deviation 5 If the histogram is not bell shaped but it is symmetric. Find the least proportion of data falls between 70 and 80 If the histogram is bell shaped. Find the proportion of data between 65 and 77...
2 answers
Johnson Corporation's bank statement for October reports an ending balance of $22,381, whereas Johnson's cash account shows a balance of $22,025 on October 31. The following additional information is available: A $855 deposit made on October 31 was not recorded by the bank until November. At the end of October, outstanding checks total $1,222. The bank statement shows bank service charges of $125 not yet recorded by the company. The company erroneously recorded as $973 a check that it had actual
Johnson Corporation's bank statement for October reports an ending balance of $22,381, whereas Johnson's cash account shows a balance of $22,025 on October 31. The following additional information is available: A $855 deposit made on October 31 was not recorded by the bank until November. At the end...
1 answer
How much weight can a man lift in the jupiter if he can lift 100kg on the earth.calculate
how much weight can a man lift in the jupiter if he can lift 100kg on the earth.calculate...
2 answers
Which of the following is most likely the next step in the series ?
which of the following is most likely the next step in the series ?...
1 answer
What is 10 squared then the cube root of that
What is 10 squared then the cube root of that...
2 answers
When you're approaching the scene of a collision on the side of the road, you should: A. Only glance at it long enough to avoid it B. Slow down while analyzing what happened C. Stop your car and volunteer to provide assistance
When you're approaching the scene of a collision on the side of the road, you should: A. Only glance at it long enough to avoid it B. Slow down while analyzing what happened C. Stop your car and volunteer to provide assistance...
1 answer
Average LCD panels are around _______________, which most monitor authorities consider excellent brightness. A. 100 kHzB. 100 bitsC. 300 pixelsD. 300 nits
Average LCD panels are around _______________, which most monitor authorities consider excellent brightness.
A. 100 kHzB. 100 bitsC. 300 pixelsD. 300 nits...
2 answers
What is the radius of a circle thats 16 units?
what is the radius of a circle thats 16 units?...
1 answer
________ are consumer products that the consumer either does not know about or knows about but does not normally think about buying. These products require a lot of advertising, personal selling, and other marketing efforts.
________ are consumer products that the consumer either does not know about or knows about but does not normally think about buying. These products require a lot of advertising, personal selling, and other marketing efforts....
2 answers
I am in a timed test please help! 3x + 12 = 21
I am in a timed test please help!
3x + 12 = 21...
1 answer
If someone is colorblind which structure is malfunctioning
if someone is colorblind which structure is malfunctioning...
1 answer
4.5. 10. A map has a scale of 1:4000 On the map, the distance between two houses is 9cm. What is the actual distance between the houses? Give your answer in metres.
4.5.
10.
A map has a scale of 1:4000
On the map, the distance between two houses is 9cm.
What is the actual distance between the houses?
Give your answer in metres....
1 answer
2. What kind of language would you expect to hear from someone with a sense of grandeur?
2. What kind of language would you expect to hear from someone with a sense of grandeur?...
1 answer
Printer: $149, 18% off DIscount price selling price
printer: $149, 18% off
DIscount price
selling price...
1 answer
Lee y escoge la opción con la forma correcta del verbo para completar la frase. Read and choose the option with the correct form of the verb to complete the sentence. Nosotros nos ________ las chaquetas, pero las olvidamos en el carro. (1 point) pondríamos pondrían pondíamos ponían
Lee y escoge la opción con la forma correcta del verbo para completar la frase. Read and choose the option with the correct form of the verb to complete the sentence.
Nosotros nos ________ las chaquetas, pero las olvidamos en el carro. (1 point)
pondríamos
pondrían
pondíamos
ponían...
2 answers
The area of the rectangle shown below is 6x2+11x-7 square units. the length is 2x-1 what is the width
The area of the rectangle shown below is 6x2+11x-7 square units. the length is 2x-1 what is the width...
1 answer
A payday loan company has decided to open several new locations in the city. To decide where to open these locations it hires consultants and pays them per store opened. At the end of the quarter, the company notices a many of the new stores’ sales volume fail to meet expectations. To incentivize the consultants to instead focus on opening profitable stores, the company should have paid them A. Per store opened B. A percentage of the profit earned per new store C. A fixed salary D. All of the
A payday loan company has decided to open several new locations in the city. To decide where to open these locations it hires consultants and pays them per store opened. At the end of the quarter, the company notices a many of the new stores’ sales volume fail to meet expectations. To incentivize ...
2 answers
What are some dangers of reduced biodiversity and modern farming practices? Check all that apply. O A. There is a loss of land through deforestation in the construction of new farms. O B. Growth hormones used on animals get into our food sources and may be affecting humans. 0 c. The use of chemical fertilizers pollutes the environment. 0 D. Monoculture crops can be easily wiped out by new diseases.
What are some dangers of reduced biodiversity and modern farming
practices?
Check all that apply.
O
A. There is a loss of land through deforestation in the construction
of new farms.
O
B. Growth hormones used on animals get into our food sources and
may be affecting humans.
0
c. The use of chemical ...