After t years, the remaining mass y (in grams)of 24 grams of a radioactive elements whose half-life is 30 years is given by $y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0$ . How much of the initial mass remains after 50 years? Round your answers to two decimal places.
A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains

Question

Quizplus · Accepted Answer

To find the remaining mass after 50 years, substitute $t = 50$ into the given formula: $y = 24 \left( \frac { 1 } { 2 } \right) ^ { 50 / 30 }$. This simplifies to $y = 24 \left( \frac { 1 } { 2 } \right) ^ { 5 / 3 }$, which calculates to approximately 7.56 grams.

After T Years, the Remaining Mass Y (In Grams)of 24 y=24(12)t/30,t≥0y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0y=24(21​)t/30,t≥0

After T Years, the Remaining Mass Y (In Grams)of 24 $y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0$