188k views
3 votes
a substance has a half-life of 40 minutes. If the substance starts with 400g, how long until there is only 2g left of the substance? (round to the nearest hundredth of a minute)

User Sam Gammon
by
8.4k points

1 Answer

5 votes

Given:

half life of substance = 40 minutes

If the substance starts with 400g ang only 2g is left.

To find the time elapsed we have:


\text{Elapsed time = }halflife*\frac{\log (\frac{start\text{ amount}}{end\text{ amount}})}{\log 2}

Thus, we have:


\begin{gathered} \text{Elapsed time = 40 }*(log((400)/(2))/\log 2) \\ \\ \text{ = 40 }*\text{ }(\log 200)/(\log 2) \end{gathered}

Solving further:


40*7.64\text{ = }305.75

Therefore, the time elapsed until there is only 2g left is 305.75 minutes

ANSWER:

305.75 minutes

User Maxbellec
by
8.1k points

Related questions

asked Oct 5, 2024 70.1k views
Logan Capaldo asked Oct 5, 2024
by Logan Capaldo
8.4k points
1 answer
1 vote
70.1k views
asked Nov 5, 2024 162k views
Tams asked Nov 5, 2024
by Tams
8.5k points
2 answers
2 votes
162k views