Paragraph Styles 2. According to data from the U.S. Health Care Financing Admini

Question

Paragraph Styles 2. According to data from the U.S. Health Care Financing Administration, the national expenditures for drugs and other medical nondurables (in billions of dollars) for selected years from 1970 to 1997 are as follows: (Note that Year is coded: 1970 is recorded simply as 70.) Year-70-80 85 87 89 . 190.-191 Spent 8.8 21.6 371 43.250.6-59.9 65.6 1275 777 834 1089 91 9293 94 95 97 Apply a test to show that the national expenditures for drugs and other medical nondurables are increasing exponentially. (4 points) a. Calculate the logarithms of the y-values and extend the table above to show the transformed data. (2 points) b. Year 70 0 85 8789 90 9192 93 949597 Spent 21.6 371 432 506 599 656 12 75 777 834 108.9 c. Plot the transformed data. Label the axes completely. (4 points)

Explanation / Answer

a) to show that the expenditure is increasing exponentially, we can plot the natural logarithm of the expenditure versus time(year). If the plot yields a straight line with constant slope, it means that the expenditure is increasing exponentially with respect to time.

Above is the semilog plot of expenditure vs year which is clearly a straight line and thus it can be concluded that that the expenditure increases exponentially.

b)

4.6904

The above table shows the natural logarithmic values of spent money indicated against the year and spent money.

c)

Above is the well labelled plot of transformed data.

Year Spent log(spent) 70 8.8 2.174752 80 21.6 3.072693 85 37.1 3.613617 87 43.2 3.76584 89 50.6 3.923952 90 59.9 4.092677 91 65.6 4.183576 92 71.2 4.265493 93 75 4.317488 94 77.7 4.352855 95 83.4 4.423648 97 108.9

4.6904

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.