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A college student is choosing between data plans for her new cell phone. Both plans include an allowance of 2 gigabytes of data per month. The monthly cost of each option can be seen as a function and represented with an equation:

Option A: A(x)=60

Option B: B(x)=10x+25

In each function, the input, x , represents the gigabytes of data used over the monthly allowance.

1. The student decides to find the values of A(1) and B(1) and compare them. What are those values?
A(1)=
B(1)=

2. After looking at some of her past phone bills, she decided to compare A(7.5) to B(7.5) . What are those values?

A(7.5)=
B(7.5)=

3. Describe each data plan in words.

4. Use graphing technology to graph each function on the same coordinate plane. Explain which plan you think she should choose.

The student only budgeted $50 a month for her cell phone. She thought, "I wonder how many gigabytes of data I would have for $50 if I go with Option B?" and wrote B(x)=50 .

B(x)=50, x=



What is the answer to her question?

Respuesta :

24nanjoshua

1. A(1) = 60 B(1) = 35

2. A(7.5) = 60 B(7.5) = 100

3. Data plan A is constantly 60 which means no added fees (good for long usage)

Data plan B constantly charges 10 with 25 as an entrance fee (good for short usage)

4. See attached files and read the text in parentheses at question 3

50 = 10x + 25 || 25 = 10x || x = 2.5

Ver imagen 24nanjoshua

The functions for the total cost per month for data use are linear in each of

the given options.

Correct responses;

  • 1. A(1) = 60,   B(1) = 35
  • 2. A(7.5) = 60,   B(7.5) = 100
  • 3. The monthly charge for Option A fixed. The monthly charge for Option B includes a fixed monthly fee and $10 per gigabyte used.
  • 4. Please find attached the combined graph of Option A and Option B. Option B is more affordable when the (extra) data usage is less than 3.5 gigabyte each month.
  • The amount of gigabyte of data the student would have for $50 is 2.5 gigabytes.

Methods by which the above values are derived

The given parameters are;

Both plans data allowance per month = 2 gigabytes

Monthly cost for each option are;

Option A: A(x) = 60 = Constant

Option B: B(x) = 10·x + 25

Solution:

1. The values of A(1) and B(1) are;

A(1) = 60

B(1) = 10 × 1 + 25 = 35

Therefore;

A(1) = $60

B(1) = $35

2. The values of A(7.5), and B(7.5) are;

A(7.5) = 60

B(7.5) = 10 × 7.5 + 25 = 100

A(7.5) = $60

B(7.5) = $100

3. The description of each data plan are;

Option A

  • The data plan of option A has a fixed charge of $60

Option B

  • The charges on the data plan on option B consist of a fixed monthly charge of $25, and $10 per gigabyte of data used.

4. Please find attached the graph of the functions of Option A and Option B. From the graph, the most affordable plan to use based on the data usage are;

  • Option B; If the data used a month, x < 3.5 gigabytes
  • Option A; If the data used a month, x > 3.5 gigabytes
  • Either Option A or Option B if the data usage per month is exactly 3.5 gigabytes

The amount the student budgets per month = $50

By using Option B, we have;

B(x) = 10·x + 25 = 50

10·x = 50 - 25 = 25

[tex]\displaystyle x = \frac{25}{10} = 2.5[/tex]

  • At $50, the amount of gigabyte the student can get is x = 2.5 gigabyte

Learn more about linear functions here:

https://brainly.com/question/8627594

Ver imagen oeerivona