The logarithmic model, y = 10.454 + 9.583 ln(x), was determined by transforming the data through natural logarithms and using linear regression. The coefficients a and b were found to be 10.454 and 9.583, respectively.
A logarithmic model is a function that has the form y = a + b ln(x), where a and b are constants. To find the missing coefficients, we can use the method of linear regression on the given data. First, we need to transform the data by taking the natural logarithm of the x-values.
Then, we can use a calculator or a software to find the best-fit line for the transformed data. The slope and the y-intercept of the line will give us the values of b and a, respectively. Here are the steps:
Transform the data by taking the natural logarithm of the x-values. The table becomes:
ln(x) y
1.099 17.4
1.504 18.6
1.792 19.7
2.014 21.0
Use a calculator or a software to find the best-fit line for the transformed data. The equation of the line is y = 10.454 + 9.583 ln(x).
The slope of the line is 9.583, which is the value of b. The y-intercept of the line is 10.454, which is the value of a.
The logarithmic model is y = 10.454 + 9.583 ln(x). Round the coefficients to 3 decimal places, we get y = 10.454 + 9.583 ln(x).