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

Explanation:

Answer 2

A decay rate of 26.3% per minute means that for every minute that passes, there remains 73.7% of the amount of the substance available at the end of the previous minute.

If
`a_0` is the starting amount, and
`a_i` is the amount left after
`i` minutes, then

`a_1=0.737a_0`

`a_2=0.737a_1=0.737^2a_0`

`a_3=0.737a_2=0.737^3a_0`

and so on, such that

`a_7=0.737^7a_0`

We have
`a_0=510` grams at the start, so after 7 minutes we're left with

`a_7=0.737^7(510)\approx60.2\,\rm g`