An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Verify that the number of loaves and cost are non-negative.
Check if the equation c = 3.5 b holds true for each pair of values in the tables.
Eliminate tables with negative values or those that do not satisfy the equation.
Identify the table that satisfies both conditions: non-negative values and the correct equation. The second table matches the equation and includes only viable solutions: T ab l e 2 .
Explanation
Understanding the Problem We are given the equation c = 3.5 b , which models the relationship between the number of loaves of bread purchased ( b ) and the total cost ( c ). We need to find the table that matches this equation and only includes viable solutions. Viable solutions mean that both the number of loaves and the cost must be non-negative, since you can't buy a negative number of loaves or have a negative cost.
Analyzing Table 1 Let's examine the first table:
Loaves ( b )
Cost ( c )
-2
-7
0
0
2
7
4
14
This table includes negative values for both loaves and cost, which are not viable. Therefore, this table does not match the requirements.
Analyzing Table 2 Now, let's check the second table:
Loaves ( b )
Cost ( c )
0
0
0.5
1.75
1
3.5
1.5
5.25
For each pair, we need to verify if c = 3.5 b .
If b = 0 , then c = 3.5 ∗ 0 = 0 . This matches the table.
If b = 0.5 , then c = 3.5 ∗ 0.5 = 1.75 . This matches the table.
If b = 1 , then c = 3.5 ∗ 1 = 3.5 . This matches the table.
If b = 1.5 , then c = 3.5 ∗ 1.5 = 5.25 . This matches the table.
All values are non-negative, and the equation holds true for all pairs. So, this table is a viable solution.
Analyzing Table 3 Finally, let's analyze the third table:
Loaves ( b )
Cost ( c )
0
0
3
10.5
6
21
9
31.5
For each pair, we need to verify if c = 3.5 b .
If b = 0 , then c = 3.5 ∗ 0 = 0 . This matches the table.
If b = 3 , then c = 3.5 ∗ 3 = 10.5 . This matches the table.
If b = 6 , then c = 3.5 ∗ 6 = 21 . This matches the table.
If b = 9 , then c = 3.5 ∗ 9 = 31.5 . This matches the table.
All values are non-negative, and the equation holds true for all pairs. So, this table is also a viable solution.
Choosing the Correct Table Both the second and third tables match the equation c = 3.5 b and include only viable solutions. However, the question asks for the table, implying there is only one correct answer. Let's re-examine the tables and the question. The question asks 'Which table of values matches the equation'. Both tables match the equation. Without further information, either table 2 or table 3 could be considered correct. However, since the tables are presented as options, and we need to choose one, let's consider the simplest or most 'basic' table. Table 2 has values 0, 0.5, 1, 1.5 which are simpler than 0, 3, 6, 9 in table 3. Therefore, we will choose table 2.
Final Answer The table that matches the equation c = 3.5 b and includes only viable solutions is the second table.
Examples
Understanding the relationship between the number of items purchased and the total cost is a fundamental concept in everyday life. For instance, if you're buying coffee beans at 12 p er ba g , yo u c an u se t h ee q u a t i o n c = 12b t o d e t er min e t h e t o t a l cos t ( c ) f or an y n u mb ero f ba g s ( b$). This helps in budgeting and making informed purchasing decisions, whether you're a consumer or a business owner managing inventory.
A current of 15.0 A flowing for 30 seconds results in a total charge of 450 Coulombs. This charge corresponds to approximately 2.81 x 10^21 electrons flowing through the device. Therefore, around 2.81 trillion electrons pass through the device during this time.
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