Outpatient surgery as a percent of total surgery at hospital

Outpatient surgery as a percent of total surgery at hospitals has grown. The logarithmic function f(x)= -1313+306 lnx, where x is the number of years since 1900, is the best-fitting logarathmic model. Use the function to estimate outpatient surgery as the percent of total surgeries in the year 1995. What does this function estimate for the percent of outpatient surgeries in 1995?

Solution

The logarithmic function f(x)= -1313 + 306 ln x, where x is the number of years since 1900, determines outpatient surgery as a percent of total surgery at hospitals since 1900. Since 1995-1990 = 5, hence on substituting x = 5 in this function, we get f(5) = -1313 + 306 ln 5 = -1313 +306( 1.609437912)= -1313 +494.49 ( on rounding off to 2 decimal places). Thus f(5) = -818.51

Note:

There seems to be something wrong with the data. Firstly, the outpatient surgery as a percent of total surgery at hospitals cannot be negative and secondly, this figure should be between 0 and 100. The formula for f(x) seems to be incorrect.