Question

A radioactive substance has a decay rate of 0.073 per minute. How many grams of a 120 gram sample will remain radioactive after 30 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.

Answer 1

Answer:

13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.

Step-by-step explanation:

Given : A radioactive substance has a decay rate of 0.073 per minute.

To find : How many grams of a 120 gram sample will remain radioactive after 30 minutes?          

Solution :

Using decaying formula,  

$y(t)=y_o e^{-rt}$

Where, $y_o=120$ is the initial amount

r=0.073 is the decay rate

t=30 minute is the time

Substitute the value in the formula,

$y(30)=120\times e^{-0.073\times 30}$

$y(30)=120\times e^{-2.19}$

$y(30)=120\times 0.1119$

$y(30)=13.428$

$y(30)=13.4$

Therefore, 13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.

Answer 2

Answer:

13.4

Step-by-step explanation:

Substitute the given values into the formula: A(t)=Pert. Where P is the initial mass, r is the rate of decay, and t is time.  Note, the rate is negative because we are finding the rate of decay.  

A=120e−(0.073)(30)≈13.4

So, about 13.4 grams will remain after 30 minutes.