APFIVE Logarithmic Derivative and Scaling Factors
A chemist analyzes the reactant concentration modeled by $$C(t)=\frac{5*t}{1+t}$$ and computes its logarithmic derivative to determine the percent rate of change. What would happen if the initial concentration is doubled, yielding $$C(t)=\frac{10*t}{1+t}$$; how is the logarithmic derivative affected?
A
It becomes variable and less predictable with the constant factor.
B
It remains unchanged because the multiplicative constant cancels out in the logarithmic derivative.
C
It doubles as the result of the increased numerator.
D
It is halved due to the proportional increase in initial concentration.
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