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

13.4

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.

Answer 2

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

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* e^(-0.073* 30)`

`y(30)=120* e^(-2.19)`

`y(30)=120* 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.