Question

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this is 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?
3 days
10 days
13 days
33 days

Answer 1

@Nnesha

Answer 2

HI!!

Answer 3

i guess you need the half life of each right?

Answer 4

yeah

Answer 5

i am trying to think of a quick way to do it, without going through the whole
\[A_0e^{kt}\] business give me a sec, otherwise we have to grind it out

Answer 6

yeah we can do it a quicker way
solve
\[\left(\frac{1}{10}\right)^{\frac{t}{33}}=\frac{1}{2}\]for \(t\) to find the half life of the first one
for the second solve \[\left(\frac{1}{10}\right)^{\frac{t}{43}}=\frac{1}{2}\]

Answer 7

so t would be the half life?

Answer 8

when you solve that, yes
you want to do it the hard way or the easy way?

Answer 9

Nope, just solved it in the calculator... it ended up being a difference of three days :)

Answer 10

Thanks so much

Answer 11

ok good

Answer 12

yeah first close to 10, second to 13
\[\color\magenta\heartsuit\]

Answer 13

yep, much faster than the normal formula