An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the rate of change using two points from the table.
Apply the formula: Rate of Change = Δ x Δ y .
Substitute the values: Rate of Change = 3 − 2 6 − 4 = 2 .
The rate of change is \boxed{$2 per song}.
Explanation
Understanding the Problem The problem provides a table showing the number of songs downloaded and the corresponding total cost. We need to find the rate of change, which represents how much the total cost changes for each additional song downloaded.
Rate of Change Formula The rate of change can be calculated using the formula: Rate of Change = Change in Number of Songs Change in Total Cost = Δ x Δ y .
Selecting Points We can pick any two points from the table to calculate the rate of change. Let's use the points (2, 4) and (3, 6). So, x 1 = 2 , y 1 = 4 , x 2 = 3 , and y 2 = 6 .
Calculating the Rate of Change Now, we plug these values into the formula: Rate of Change = 3 − 2 6 − 4 = 1 2 = 2 .
Interpreting the Result The rate of change is 2, which means the cost increases by $2 for each additional song downloaded. Therefore, the rate of change is $2 per song.
Final Answer The rate of change for the function in the table is $2 per song.
Examples
Imagine you're at a music store where each song costs the same to download. Knowing the rate of change ($2 per song) helps you quickly calculate how much it will cost to download a certain number of songs. For example, if you want to download 7 songs, you can easily estimate the cost to be $2 \times 7 = $14. This concept is useful in budgeting and making informed purchasing decisions.
A current of 15.0 A flowing for 30 seconds corresponds to a total charge of 450 Coulombs. This charge translates to approximately 2.81 x 10^{21} electrons flowing through the device. Thus, around 2.81 sextillion electrons move in this timeframe.
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