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C=60+0.05d The equation above represen...

`C=60+0.05d`
The equation above represents the total monthly cost, C, in dollars of a data plan offered by a cell phone company when the data usage in a month exceeds a 1 gigabyte limit by d megabytes. According to the model, what is the meaning of 0.05?

A

The cost per megabyte of data used

B

The cost per gigabyte of data used

C

The cost per megabyte of data after one gigabyte of data is used.

D

The cost of each additional gigabyte of data after the first megabyte of data is used.

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The correct Answer is:
To solve the question regarding the meaning of 0.05 in the equation \( C = 60 + 0.05d \), let's break it down step by step. ### Step 1: Understand the equation The equation \( C = 60 + 0.05d \) represents the total monthly cost \( C \) in dollars for a data plan. Here, \( d \) represents the amount of data usage in megabytes that exceeds a 1 gigabyte limit. **Hint:** Identify the components of the equation and what each variable represents. ### Step 2: Analyze the constant term The constant term \( 60 \) represents the base cost of the data plan up to the 1 gigabyte limit. This means that for the first 1 gigabyte of data usage, the user pays $60. **Hint:** Recognize that the constant part of the equation indicates the cost before any additional data usage. ### Step 3: Examine the variable term The term \( 0.05d \) indicates the additional cost incurred for every megabyte \( d \) that exceeds the 1 gigabyte limit. The coefficient \( 0.05 \) tells us how much extra the user has to pay for each megabyte over the limit. **Hint:** Focus on the variable part of the equation to understand how costs change with additional data usage. ### Step 4: Interpret the coefficient Since \( 0.05 \) is the coefficient of \( d \), it represents the cost per megabyte for data usage beyond the initial 1 gigabyte. Therefore, for every megabyte that exceeds the limit, the user pays an additional $0.05. **Hint:** Relate the coefficient to the cost structure of the data plan. ### Conclusion Thus, the meaning of \( 0.05 \) in the equation is that it represents the cost per megabyte of data usage after the initial 1 gigabyte limit has been exceeded. **Final Answer:** The cost per megabyte of data after 1 gigabyte of data is used.
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