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 profit per album: P ro f i t = S e ll in g P r i ce − P r in t in g C os t = $8.62 .
Calculate the cumulative profit for each month by subtracting the initial cost and monthly expenses from the monthly revenue.
Determine the month when the cumulative profit becomes non-negative.
Kesia Records first breaks even in May, with a cumulative profit of M a y .
Explanation
Problem Analysis Let's analyze the problem. Kesia Records needs to cover the initial cost of the album rights, the printing costs, and the monthly expenses. We need to find the month when the cumulative profit becomes non-negative.
Profit Per Album First, calculate the profit per album: P ro f i t _ p er _ a l b u m = S e ll in g _ p r i ce − P r in t in g _ cos t = $9.75 − $1.13 = $8.62
Monthly Revenue and Cumulative Profit Now, let's calculate the monthly revenue and cumulative profit for each month, taking into account the initial cost of the album rights ($148,950).
Calculating Cumulative Profit for Each Month
January:
Albums sold: 5,486
Revenue: 5486 × $8.62 = $47 , 281.32
Expenses: $27,714
Initial cost: $148,950
Profit: 47 , 281.32 − $27 , 714 − $148 , 950 = − $129 , 382.68
Cumulative Profit: -$129,382.68
February:
Albums sold: 8,191
Revenue: 8191 × $8.62 = $70 , 604.42
Expenses: $21,689
Profit: 70 , 604.42 − $21 , 689 = $48 , 915.42
Cumulative Profit: - 129 , 382.68 + $48 , 915.42 = − $80 , 467.26
March:
Albums sold: 4,796
Revenue: 4796 × $8.62 = $41 , 335.52
Expenses: $25,195
Profit: 41 , 335.52 − $25 , 195 = $16 , 140.52
Cumulative Profit: - 80 , 467.26 + $16 , 140.52 = − $64 , 326.74
April:
Albums sold: 7,490
Revenue: 7490 × $8.62 = $64 , 563.80
Expenses: $28,766
Profit: 64 , 563.80 − $28 , 766 = $35 , 797.80
Cumulative Profit: - 64 , 326.74 + $35 , 797.80 = − $28 , 528.94
May:
Albums sold: 6,272
Revenue: 6272 × $8.62 = $54 , 068.64
Expenses: $24,604
Profit: 54 , 068.64 − $24 , 604 = $29 , 464.64
Cumulative Profit: - 28 , 528.94 + $29 , 464.64 = $935.70
June:
Albums sold: 5,131
Revenue: 5131 × $8.62 = $44 , 229.22
Expenses: $29,040
Profit: 44 , 229.22 − $29 , 040 = $15 , 189.22
Cumulative Profit: $935.70 + $15,189.22 = $16,124.92
Break-Even Point Kesia Records first broke even in May, as the cumulative profit becomes positive in that month.
Examples
Understanding break-even points is crucial in business. For example, if you're starting a lemonade stand, you need to know how many cups you must sell to cover your initial costs (lemons, sugar, cups) and ongoing expenses. By calculating your profit per cup and tracking your sales and expenses, you can determine when your lemonade stand starts making a profit. This concept applies to larger businesses as well, helping them make informed decisions about pricing, production, and investments.
In 30 seconds, about 2.81 x 10^21 electrons flow through the device. This was determined by calculating the total charge delivered at a current of 15.0 A and converting that charge to the number of electrons using the charge of a single electron. Thus, using the relationship between current, charge, and the charge of an electron, we derived the total electron flow.
;
