the function ( t = f(a) ) models the time, in minutes, for a chemical reaction to occur as a function of the…

the function ( t = f(a) ) models the time, in minutes, for a chemical reaction to occur as a function of the amount ( a ) of catalyst used, measured in milliliters. what are the units for ( f(a) )?\na minutes per milliliter\nb milliliters per minute\nc minutes per milliliter per milliliter\nd milliliters per minute per minute

the function ( t = f(a) ) models the time, in minutes, for a chemical reaction to occur as a function of the amount ( a ) of catalyst used, measured in milliliters. what are the units for ( f(a) )?\na minutes per milliliter\nb milliliters per minute\nc minutes per milliliter per milliliter\nd milliliters per minute per minute

Answer

Answer:

C. minutes per milliliter per milliliter

Explanation:

Step1: Recall the units of the first - derivative

The first - derivative (f^{\prime}(A)=\frac{df}{dA}). Since (t = f(A)) where (t) (the dependent variable) has units of minutes and (A) (the independent variable) has units of milliliters, the units of (f^{\prime}(A)) are (\frac{\text{minutes}}{\text{milliliters}}) (minutes per milliliter).

Step2: Find the units of the second - derivative

The second - derivative (f^{\prime\prime}(A)=\frac{d}{dA}(f^{\prime}(A))). Let (y = f^{\prime}(A)) with (y) having units (\frac{\text{minutes}}{\text{milliliters}}) and the variable of differentiation is still (A) (units of milliliters). Then (f^{\prime\prime}(A)=\frac{dy}{dA}), and the units of (f^{\prime\prime}(A)) are (\frac{\frac{\text{minutes}}{\text{milliliters}}}{\text{milliliters}}=\frac{\text{minutes}}{\text{milliliters}\times\text{milliliters}}) (minutes per milliliter per milliliter).