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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).

2 Answers

2 votes

Answer: 368.8

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

1400(0.92)^17-1

≈368.8

User Nirav Bhatt
by
8.2k points
4 votes

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

User Henrique Branco
by
9.0k points

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