An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
When an electric device delivers a current of 15.0 A for 30 seconds, approximately 2.81 billion billion electrons flow through it. This is calculated by first finding the total charge using the formula Q = I × t and then dividing by the charge of a single electron. The final result shows that about 2.81 x 10^21 electrons pass through the device during that time.
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Calculate the profit increase from year to year.
Calculate the average profit increase over the 4 years: \frac{$3,915.20 + $4,267.57 + $4,651.66 + $5,070.30}{4} = $4,476.1825
Add the average profit increase to the profit of Year 5 to estimate the profit for the next year: $61,406.98 + $4,476.1825 = $65,883.1625
Rounding to the nearest cent, the estimated profit for the next year is $\boxed{ 65,883.16} .
Explanation
Problem Analysis We are given the net profits for Sam's swimming pool cleaning business over the past 5 years and want to estimate the profit for the next year. To do this, we will calculate the year-to-year profit increases, find the average of these increases, and add that average to the most recent year's profit.
Calculating Yearly Profit Increases First, we calculate the profit increase from year to year:
Year 2 - Year 1: $47,417.45 - $43,502.25 = $3,915.20
Year 3 - Year 2: $51,685.02 - $47,417.45 = $4,267.57
Year 4 - Year 3: $56,336.68 - $51,685.02 = $4,651.66
Year 5 - Year 4: $61,406.98 - $56,336.68 = $5,070.30
Finding the Average Profit Increase Next, we calculate the average profit increase over the 4 years:
Average Increase = ($3,915.20 + $4,267.57 + $4,651.66 + $5,070.30) / 4 = $4,476.1825
Estimating Next Year's Profit Now, we add the average profit increase to the profit of Year 5 to estimate the profit for the next year:
Estimated Profit = $61,406.98 + $4,476.1825 = $65,883.1625
Rounding to the nearest cent, the estimated profit for the next year is $65,883.16.
Determining the Best Estimate The best estimate for Sam to quote as expected profits in the next year in his new business plan is approximately $65,883.16. Looking at the multiple choice options, the closest answer is a. $66,477.28. However, our calculated estimate is significantly different from all the options. Let's re-examine the calculations to ensure accuracy.
Final Answer and Conclusion Upon re-examining the calculations, it appears there was a slight error in the final rounding and comparison with the options. The correct estimated profit is indeed approximately $65,883.16. However, since we must choose from the given options, we should select the one closest to our calculated value.
Examples
Estimating future profits based on past performance is a common practice in business. For example, a bakery owner might track their monthly sales for the past year. By analyzing the sales trends (e.g., calculating the average monthly increase), they can estimate their sales for the upcoming months. This helps in making informed decisions about inventory, staffing, and marketing strategies. Similarly, a freelance writer can track their earnings per project over time to predict their income for the next quarter, aiding in financial planning and goal setting.
