Question

An element with

mass 510 grams decays by 26.3% per minute. How much of the
element is remaining after 7 minutes, to the nearest 10th of a gram?

Answer 1

60.2 grams is remaining after 7 minutes.

Explanation:

Exponential equation for amount of substance:

The exponential equation for the amount of a substance is given by:

`A(t) = A(0)(1-r)^t`

In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time measure.

An element with mass 510 grams decays by 26.3% per minute.

This means that
`A(0) = 510, r = 0.263`

So

`A(t) = A(0)(1-r)^t`

`A(t) = 510(1-0.263)^t`

`A(t) = 510(0.737)^t`

How much of the element is remaining after 7 minutes?

This is A(7). So

`A(7) = 510(0.737)^7 = 60.2`

60.2 grams is remaining after 7 minutes.