Concept explainers
(a)
To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by
(b)
To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by
(c)
To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by
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Mathematical Applications for the Management, Life, and Social Sciences
- Farms in the United States The graph gives the number of farms in the United States from 1850 to 2000. aEstimate the average rate of change in the number of farms between i 1860 and 1890 and ii 1950 and 1970. bIn which decade did the number of farms experience the greatest average rate of decline?arrow_forwardUse the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.arrow_forwardWhen Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data are not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of change is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change from 2 to 5 is not the same as the average rate of change from 5 to 6. This shows that the data are not linear, even though the differences in y are constant. x 1 2 5 6 y 3 6 9 12arrow_forward
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