Radioactive gold (195Au-aurothiomalate) has an affinity for inflamed tissues and is sometimes used as a racer to diagnose arthritis. The data in the following table (62) come from an experiment investigating the length of time and the concentrations that 195Au-aurothiomalate is retained in a person’s blood. Listed are the serum gold concentrations found in ten blood samples taken from patients given an initial dose of 50 mg. Follow-up readings were made at various times, ranging from one to seven days after injection. In each case, the retention is expressed as a percentage of the patient’s day-zero serum gold concentration.

Days after Injection, x          Serum Gold %

Concentration, y

1……………………………  94.5

1……………………………  86.4

2……………………………  71.0

2……………………………  80.5

2……………………………  81.4

3……………………………  67.4

5……………………………  49.3

6……………………………  46.8

6……………………………  42.3

7……………………………  36.6

(a) Fit an exponential curve to these data.

(b) Estimate the half-life of 195Au-aurothiomalate; that is, how long does it take for half the gold to disappear from a person’s blood?

If x denotes days after injection and y denotes serum gold % concentration, then = 35,= 169, ln yi = 41.35720, and  ln y_i = 137.97415.

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