A phone company offers a monthly data plan for $10 a month. The plan includes 2 megabytes of data, and charges $0.10 per megabytes above the 2 megabytes of data. Write a piece-wise defined function for T(x), the cost for x megabytes of data used in a month.

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avortarF · Accepted Answer

Since the cost is $10 per month for the first 2 megabytes, then T(x)=10 for 0≤x≤2 where xx is the number of megabytes used. Since the monthly plan fee includes the first 2 megabytes, then the additional fee is only charged for x−2 megabytes when x&amp;gt;2. The additional fee is $0.10 per megabyte so the additional fee forx−2 megabytes is 0.10(x−2)=0.1x−0.2 dollars. Adding this to the monthly fee gives a total cost of T(x)=10+0.1x−0.2=0.1x+9.8 for x&amp;gt;2. The piecewise function is then T(x)=100≤x≤2,0.1x+9.8x&amp;gt;2

nick1337 · Accepted Answer

Answer:T(x)={100if&amp;nbsp;0≤x≤20.1x+9.8if&amp;nbsp;x&amp;gt;2Explanation:The cost function for x megabytes of data used in a month can be defined as follows:T(x)={100if&amp;nbsp;0≤x≤20.1x+9.8if&amp;nbsp;x&amp;gt;2In this piece-wise defined function, if the data usage x is between 0 and 2 megabytes (inclusive), the cost is a fixed 10. This is represented by the equation T(x)=100 for 0≤x≤2.On the other hand, if the data usage x is greater than 2 megabytes, the cost is calculated by adding a fixed base cost of 9.8 to the variable cost of 0.1 per megabyte. This is represented by the equation T(x)=0.1x+9.8 for x&amp;gt;2.Therefore, the piece-wise defined function for the cost of x megabytes of data used in a month is T(x)={100if&amp;nbsp;0≤x≤20.1x+9.8if&amp;nbsp;x&amp;gt;2.

Vasquez · Accepted Answer

For 0≤x≤2, where x represents the number of megabytes of data used in a month, the cost is T(x)=10. This is because the plan includes 2 megabytes of data, and the cost remains constant regardless of the amount of data used within this range.For x&amp;gt;2, the cost increases as additional data is used. The cost per megabyte above the initial 2 megabytes is 0.10. Therefore, for each additional megabyte, the cost is 0.10×x. However, since the plan already covers the initial 2 megabytes, we subtract the cost of those 2 megabytes, resulting in 0.10×(x−2).To obtain the complete expression, we add the constant cost of 10 to the variable cost of 0.10×(x−2), giving us T(x)=0.10×(x−2)+10. Simplifying this equation yields T(x)=0.10x−0.20+10, which can be further simplified as T(x)=0.10x+9.80.Therefore, the piece-wise defined function for the cost T(x), where x represents the number of megabytes of data used in a month, is:T(x)={10,if&amp;nbsp;0≤x≤20.10x+9.80,if&amp;nbsp;x&amp;gt;2

Don Sumner · Accepted Answer

The cost function, denoted as T(x), can be defined as a piece-wise function to account for the different scenarios of data usage:T(x)={10if&amp;nbsp;x≤2,10+0.10(x−2)if&amp;nbsp;x&amp;gt;2.Let&#039;s break down the function:- If the data usage, denoted as x, is less than or equal to 2 megabytes, the cost is a flat fee of 10 per month. This is represented by the first case where x≤2.- If the data usage exceeds 2 megabytes, there is an additional charge of 0.10 per megabyte for the extra data used. The cost for this scenario can be calculated by taking the difference between the total data usage (x) and the initial 2 megabytes, multiplying it by 0.10, and adding it to the base fee of 10. This is represented by the second case where x&amp;gt;2.By using this piece-wise function, you can determine the cost (T(x)) for any given amount of data usage (x) in a month.

A phone company offers a monthly data plan for $10 a month. The plan includes 2 megabytes of data, and charges $0.10 per megabytes above the 2 megabytes of data. Write a piece-wise defined function for T(x), the cost for x megabytes of data used in a month.

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