Step 1 :Given that the initial mass of the substance, \( P_0 \), is 21 grams, the growth rate, \( r \), is 0.14 (14% expressed as a decimal), and the time, \( t \), is 6 days.
Step 2 :We can use the formula for exponential growth to find the mass of the substance after six days: \[ P(t) = P_0 * e^{rt} \] where \( P(t) \) is the final amount at time \( t \), \( P_0 \) is the initial amount, \( r \) is the growth rate, and \( t \) is the time.
Step 3 :Substitute the given values into the formula: \[ P(t) = 21 * e^{0.14*6} \]
Step 4 :Solving the equation gives the mass of the substance after six days: \[ P_t = 48.6 \]
Step 5 :Final Answer: The mass of the sample after six days is \(\boxed{48.6}\) grams.