Question

In a lab experiment, the decay of a radioactive isotope is being observed. At the

beginning of the first day of the experiment the mass of the substance was 1500
grams and mass was decreasing by 8% per day. Determine the mass of the radioactive
sample at the beginning of the 20th day of the experiment. Round to the nearest
tenth (if necessary).

Answer 1

Answer: 368.8

Step-by-step explanation: Explicit Formula: a^n=a^1r^n-1

1400(0.92)^17-1

​

≈368.8

Answer 2

Answer: 307.7 grams

Explanation:

The exponential decay equation with initial value 'A' and rate of decay 'r' ( in decimal) in 't' years is given by :-

`M(t)=A(1-r)^t\quad...(i)`

As per given , we have

Initial mass of isotope = 1500 grams

Rate of decay : r= 8% =0.08

To find : the mass of the radioactive sample at the beginning of the 20th day of the experiment ( i.e. after 19 days).

That would be ,

`M(19)=1500(1-0.08)^(19)` [Using (i)]

`M(19)=307.652167113\approx307.7` [Rounded to the nearest tenth]

Hence, the mass of the radioactive sample at the beginning of the 20th day of the experiment = 307.7 grams