An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The student earns $12 per hour, so the earnings from hourly rate is 12 h .
The student earns $0.50 for each bakery item, which is 2 b .
The student earns $0.25 for each drink, which is 4 d .
The total earnings function is the sum of these: T = 12 h + 2 b + 4 d , so the answer is C .
Explanation
Understanding the Earnings Components Let's break down how the student's earnings are calculated. He has a fixed hourly rate, plus additional income from selling bakery items and drinks. We need to combine these to find the total earnings function.
Calculating Hourly Earnings The student earns $12 for each hour worked, which can be represented as 12 × h or 12 h .
Calculating Bakery Item Earnings He also earns $0.50 for each bakery item sold, which can be written as 0.50 × b . Since 0.50 is the same as 2 1 , this can also be written as 2 b .
Calculating Drink Earnings Additionally, he earns $0.25 for each drink sold, which is 0.25 × d . Since 0.25 is the same as 4 1 , this can also be written as 4 d .
Combining Earnings for the Total Function To find the total earnings, we add up the earnings from each source: hourly, bakery items, and drinks. This gives us the function: T = 12 h + 2 b + 4 d .
Identifying the Correct Option Comparing our derived function T = 12 h + 2 b + 4 d with the given options, we see that it matches option C.
Examples
Imagine you're running a lemonade stand. You charge a fixed amount per hour to set up and manage the stand, plus extra for each cup of lemonade and cookie you sell. The earnings function helps you calculate your total income based on the hours you work, the number of lemonade cups you sell, and the number of cookies you sell. This is similar to how the student's earnings are calculated at the school play, combining an hourly wage with sales commissions. Understanding how to create such functions is useful in many real-world scenarios, from managing a small business to understanding your own paycheck!
Approximately 2.81 × 1 0 21 electrons flow through the device delivering a current of 15.0 A for 30 seconds, as we calculated using the relationship between charge and current. The total charge was found to be 450 C , which we divided by the charge of a single electron to get the number of electrons. This demonstrates the connection between current, charge, and the number of electrons in an electric circuit.
;
