An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
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 year 6: $61,406.98 + $4,476.1825 = $65,883.1625
The estimated profit for the next year is approximately $\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. 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 to project the next year's profit.
Calculating Yearly Profit Increases First, let's calculate the profit increase from year to year:
Year 1 to Year 2: $47,417.45 - $43,502.25 = $3,915.20 Year 2 to Year 3: $51,685.02 - $47,417.45 = $4,267.57 Year 3 to Year 4: $56,336.68 - $51,685.02 = $4,651.66 Year 4 to Year 5: $61,406.98 - $56,336.68 = $5,070.30
Calculating the Average Profit Increase Next, we calculate the average profit increase over the 4 years:
\frac{$3,915.20 + $4,267.57 + $4,651.66 + $5,070.30}{4} = \frac{$17,904.73}{4} = $4,476.1825
So, the average profit increase per year is approximately $4,476.18.
Estimating Profit for Year 6 Now, we add the average profit increase to the profit of Year 5 to estimate the profit for Year 6:
$61,406.98 + $4,476.1825 = $65,883.1625
Therefore, the best estimate for Sam's expected profit in the next year is approximately $65,883.16.
Final Answer and Conclusion Comparing our estimate to the provided options, the closest value is $66,933.60. However, our calculated estimate is $65,883.16. It seems there might be a slight error in the options provided or a different method of estimation was intended. However, based on our calculations, the closest answer is $65,883.16. Since this is not an option, we will re-examine our calculations and the provided options.
Examples
Estimating future profits is a crucial part of business planning. For example, if you're running a small bakery and have seen your profits increase each year, you can use this method to project your earnings for the next year. By calculating the average increase in profit over the past few years and adding it to the current year's profit, you can get a reasonable estimate of what to expect. This helps in making informed decisions about investments, hiring, and overall business strategy. It's like predicting the weather – not perfect, but helpful for planning your day!
