The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. A sample increases continuously at a relative rate of $14 \%$ per day. Find the mass of the sample after six days if there were 21 grams of the substance present at the beginning of the study.
Do not round any intermediate computations, and round your answer to the nearest tenth.

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.