Research & Development: Federal The following table shows the total sp...

Research & Development: Federal The following table shows the total spent on research and development by the

Federal government in the United States, in billions of dollars, for the period 1995–2009 (t is the year since 1990).

Find the logarithmic regression model of the form S(t) = A ln t + C with coefficients A and C rounded to 2 decimal places. Also obtain a graph showing the data points and the regression curve. In which direction is it more reasonable to extrapolate the model? Why? HINT [See Example 5.]

Example 5:

The following table shows the total spent on research and development in the United States, in billions of dollars, for the period 1995–2009 (t is the year since 1990).*

Find the best-fit logarithmic model of the form

S(t) = A ln t + C

and use the model to project total spending on research in 2012, assuming the trend continues.

Solution We use technology to get the following regression model:

S(t) = 83.01 ln t + 64.42. Coefficients rounded

Because 2012 is represented by t = 22, we have

S(22) = 83.01 ln(22) + 64.42 ≈ 320. Why did we round the result to two significant digits?

So, research and development spending is projected to be around $321 billion in 2012.