Question

An element with mass 820 grams decays by 26.8% per minute. How much of the element is remaining after 18 minutes, to the nearest 10th of a gram?

Answer 1

Answer: 3.0

Explanation:

a=820

r= rate= 26.8%=0.268

b=1-r=1-0.268=0.732

y=820(0.732)^18

y=2.985474

y=3

Answer 2

3.0 grams of the element are left after 18 minutes

Explanation:

Recall that an exponential decay that can be studied with the following formula for the amount of material (A) as a function of time (t):

`A(t)=A_0(1-r)^t`

where:

`A_0` is the starting amount of the substance (in our case 820 grams)

r is the rate of decay (which in our case given as 26.8% can be written in decimal form as 0.268

and t is the time in minutes (in our case t = 18 minutes)

Then we have:

`A(t)=A_0(1-r)^t\\A(18)=820*(1-0.268)^18\\A(18)=820*(0.732)^18\\\\A(18)=2.985\,grams`

which can be rounded to 3.0 grams