Question

An element with mass 490 grams decays by 28.6% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

Answer 1

2.2 grams

Explanation:

We can use the compound decay formula shown below to solve this:

`F=P(1-r)^t`

Where

F is the final amount (what we want to find)

P is the present amount (490 grams)

r is the rate of decay, in decimal (28.6% = 28.6/100 = 0.286)

t is the time in minutes (16)

Substituting, we get:

`F=P(1-r)^t\\F=490(1-0.286)^(16)\\F=490(0.714)^(16)\\F=2.2355`

So, after 16 minutes, 2.2355 grams will be remaining.

Rounded to nearest tenth of a gram (1 decimal place) = 2.2 grams remaining