Jim, working with a sample of 131 Iin the lab, measures the decay rate at the end of each...

Jim, working with a sample of 131 Iin the lab, measures the decay rate at the end of each day.

Like any modem scientist, Jim wants to use all of the data instead of only two points to estimate the constants R0 and λ in equation. He will use the technique of regression to do so. Use the first method in the following list that your technology makes available to you to estimate λ (and R0 at the same time). Use this estimate to approximate the half-life of 131 I.

(a) Some modem calculators and the spreadsheet Excel can do an exponential regression to directly estimate R0 and λ.

(b) Taking the natural logarithm of both sides of equation produces the result

Now ln R is a linear function of t. Most calculators, numerical software such as MATLAB®, and computer algebra systems such as Mathematica and Maple will do a linear regression, enabling you to estimate ln R0 and λ (e.g., use the MATLAB® command polyfit).

(c) If all else fails, plotting the natural logarithm of the decay rates versus the time will produce a curve that is almost linear. Draw the straight line that in your estimation provides the best fit. The slope of this line provides an estimate of –λ.