Question

A college student is choosing between two data plans for her 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.

What are those values for A(1) and B(1)?

A. A(1) = 60, B(1) = 35
B. A(1) = 60, B(1) = 10
C. A(1) = 10, B(1) = 60
D. A(1) = 35, B(1) = 60

After looking at some of her past phone bills, she decided to compare A(7.5) and B(7.5). What are those values?
A. A(7.5) = 75, B(7.5) = 100
B. A(7.5) = 60, B(7.5) = 75
C. A(7.5) = 135, B(7.5) = 100
D. A(7.5) = 75, B(7.5) = 135

Describe each data plan in words!
Option A: A(x) = $60 for 2GB of data.
Option B: B(x) = $25 plus $10 per additional GB of data.

Graph each function on the same coordinate plane. (On a word document, click insert -> shape -> line)

Based on the graph and the information you found above, which data plan do you think she should choose and why?

A. Option A because it's cheaper for 2GB of data.
B. Option B because it's cheaper for 2GB of data.
C. Option A because it offers more data for the same price.
D. Option B because it offers more data for the same price.

Answer 1

The correct answer is A. A(1) = 60, B(1) = 35.

The correct answer is A. A(7.5) = 60, B(7.5) = 100.

Option A charges a fixed $60 per month, while Option B has a base cost of $25 and charges an additional $10 for each additional GB of data used beyond the 2GB allowance.

How to determine the values for A(1) and B(1)

To determine the values for A(1) and B(1), substitute x = 1 into the respective equations for Option A and Option B.

Option A: A(x) = 60

Substituting x = 1: A(1) = 60

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

Substituting x = 1: B(1) = 10(1) + 25 = 10 + 25 = 35

Therefore, the correct values are:

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

The correct answer is A. A(1) = 60, B(1) = 35.

To find the values for A(7.5) and B(7.5), substitute x = 7.5 into the equations for Option A and Option B.

Option A: A(x) = 60

Substituting x = 7.5: A(7.5) = 60

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

Substituting x = 7.5: B(7.5) = 10(7.5) + 25 = 75 + 25 = 100

Therefore, the correct values are:

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

The correct answer is A. A(7.5) = 60, B(7.5) = 100.

Now, describe each data plan:

Option A: For Option A, the monthly cost is a fixed amount of $60, regardless of the amount of data used. The plan includes an allowance of 2GB of data per month.

Option B: For Option B, the monthly cost is $25 plus an additional $10 for each additional gigabyte (GB) of data used beyond the 2GB allowance. The plan also includes an allowance of 2GB of data per month.

In summary, Option A charges a fixed $60 per month, while Option B has a base cost of $25 and charges an additional $10 for each additional GB of data used beyond the 2GB allowance.