APFIVE Logarithmic Derivative and Scaling Factors
A chemist analyzes the percent rate of change for a reactant’s concentration, modeled by the function $$C(t)=\frac{5*t}{1+t}$$. The percent rate of change is determined using the logarithmic derivative of $C(t)$. If a change in experimental conditions leads to a new model, $$C_{new}(t)=\frac{10*t}{1+t}$$, how is the logarithmic derivative affected?
A
It doubles as the result of the increased numerator.
B
It is halved due to the proportional increase in initial concentration.
C
It remains unchanged because the multiplicative constant cancels out in the logarithmic derivative.
D
It becomes variable and less predictable with the constant factor.
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