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 1200 grams and mass was decreasing by 10% per day. Determine the mass of the radioactive sample at the beginning of the 19th day of the experiment. Round to the nearest tenth (if necessary).

Answer 1

180.1 g

Explanation:

You want to know the mass of a radioactive isotope on the 19th day if it was 1200 g on the first day and decreased 10% per day.

Exponential decay

The form of the equation for exponential decay is ...

m(t) = a·b^(t-n)

where m is the remaining mass, 'a' is the amount on day n, and 'b' is the growth factor, equal to 1 plus the growth rate.

Application

Here, we have a=1200 g on day n=1, and the growth rate is -10%, so ...

b = 1 -0.10 = 0.90

That means ...

m(t) = 1200·(0.90^(t -1))

On day 19, the beginning amount is ...

m(19) = 1200·0.90^18 ≈ 180.1 . . . . grams

The mass of the sample at the beginning of day 19 is 180.1 grams.

<95141404393>