In a chemical reaction run at a certain temperature, the concentration C of a certain reactant at time t is given by 
where 
is the initial concentration and k is the rate constant. Assume the initial concentration is known to be 0.04 mol/L exactly. Assume that time is measured with negligible uncertainty.
a. After 30 s, the concentration C is measured to be 0.0038 ± 2.0 × 
. Estimate the rate constant k, and find the relative uncertainty in the estimate.
b. After 50 s, the concentration C is measured to be 0.0024 ± 2.0 ×. Estimate the rate constant k and find the relative uncertainty in the estimate.
c. Denote the estimates of the rate constant k in parts (a) and (b) by 
respectively. The geometric mean 
is used as an estimate of k. Find the relative uncertainty in this estimate.
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