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

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

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