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?

Respuesta :

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 [tex]a_0[/tex] is the starting amount, and [tex]a_i[/tex] is the amount left after [tex]i[/tex] minutes, then

[tex]a_1=0.737a_0[/tex]

[tex]a_2=0.737a_1=0.737^2a_0[/tex]

[tex]a_3=0.737a_2=0.737^3a_0[/tex]

and so on, such that

[tex]a_7=0.737^7a_0[/tex]

We have [tex]a_0=510[/tex] grams at the start, so after 7 minutes we're left with

[tex]a_7=0.737^7(510)\approx60.2\,\rm g[/tex]

Answer:

60.2

Step-by-step explanation:

Q&A Education