We have the following monthly sales data on gizmos. We want to find the rate of change of monthly sales. If we look at a graph of the sales data.
I can see that sales are trending upwards, but there is a seasonal variation added in. Excel will not do a good job of modeling this function with a trendline. Thus, I want to find a rate of change over a period of 12 months to eliminate the seasonal variation. To find the most recent trend I use the most recent data with a time period of 12 months. It is worth noting that the need to adjust for the right time period for comparisons is probably the reason that company revenue reports typically show the previous quarter as well as the quarter from a year earlier.
When creating marginal functions or other difference quotients, we often want the computations kept in one row, particularly if we want to graph the function and the marginal function together. A careful arrangement of the columns and the use of quick fill will make our life easier.
Use algebra to find a formula for the marginal function. From the shape of the graph of the marginal function, decide what kind of graph it appears to be. List the regions where the original function is increasing and the regions where it is decreasing.
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List the regions where the marginal function is positive and where the marginal function is negative. The table and the graph indicate that the marginal function is a constant 23 to be precise. Assuming the function is of the kind specified; find a best fitting curve for the function and a formula. In a textbox, describe your conclusions about the sign of the marginal function and the rising or falling of the original function.
Assume profit q is a polynomial function of degree 2 and that you have the following data:. Assume ResaleValue q is an exponential function and that you have the following data:.
It appears that Marginal Resale Value is always negative and Resale value is always decreasing. Assume retirementBalance q is an exponential function and that you have the following data:. Plot the revenue and marginal revenue. Explain why marginal revenue is not a good indicator of growth. Plot average rate of change over a month span and explain why it is a better measure of growth.
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Marginal Revenue is the change in revenue each month. This gives us some idea of what is happening each month, but does not give a very clear picture of overall trends.
calculus - Given the Marginal Cost Function, Calculate Marginal Profit - Mathematics Stack Exchange
The overall growth over an entire year gives a better indication of trends. Historical data for quarterly revenue reports for Microsoft can be found online. A good source is http: Plot 5 years of data. Explain why looking at marginal change of revenue from one quarter to the next is misleading.
In finance and economics this issue is dealt with using marginal functions. Thus the formulas for revenue and profit are: In setting up the spreadsheet, there are some details to notice. I have the following data on profit and production level for widgets. Make a chart of the function and the marginal function as q goes from 0 to Plot the function and the marginal function on the same graph. Find the formula for a best fitting curve for the marginal function. For problems you are given data for a function.
Quantiy 30 48 73 Profit Solution The best fitting curve is: By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Home Questions Tags Users Unanswered.
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Looks good to me. For this sort of question that revolves around whether the error is in your work or in the problem, it always helps to present the problem as verbatim as you possibly can. Thanks for the help. I just used the notation out of habit, I haven't been in a class that used discrete values in a while and felt that verifying the concept was more important than the actual values in this case.
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