OpenStudy (yuii):

Cobalt-60 has a half-life of about 5 years. How many grams of a 300 g sample will remain after 20 years? A. 0.0625 g B. 9.375 g C. 18.75 g D. 37.5 g

10 months ago
OpenStudy (yuii):

C?

10 months ago
OpenStudy (mathmale):

I'd be happy to give you feedback if you'd share the work you've done that indicates that C is the answer.

10 months ago
OpenStudy (mathmale):

Generally, you need to figure out / obtain the pertinent "decay constant" when discussing "half life." Exponential decay:\[A=A _{0}e ^{kt}\] were "k" is the decay constant and is negative.

10 months ago
OpenStudy (mathmale):

Let \[A=\frac{ 1 }{ 2 }A _{0}\] Subst. 5 years for t. Find k.

10 months ago
OpenStudy (wolf1728):

or this formula k = ln (.5) / half-life

10 months ago
OpenStudy (mathmale):

Yes, that'd be a bit faster. Thank you.

10 months ago
OpenStudy (wolf1728):

k = -0.1386294361

10 months ago
OpenStudy (irishboy123):

the observed relationship , ie "Cobalt-60 has a half-life of about 5 years"is: \(C(t) \approx C_o \left( \dfrac{1}{2} \right)^{t/5}\) where t is measured in years that is the observed and fundamental relationship. it is easy to transfer that into variations of e and so on. but you may also just say that \(C(20) = C_o \left( \dfrac{1}{2} \right)^{20/5}\)

10 months ago
OpenStudy (irishboy123):

So for 300g and 20y we test it \[C(20) = 300 \left( \dfrac{1}{2} \right)^{20/5}\] which is C

10 months ago
OpenStudy (wolf1728):

ending amt = bgn * (2.71828^(k * time)) ending amt = 300 * (2.71828^( -0.1386294361 * 20)) ending amt = 300 * (2.71828^(-2.7725887222)) ending amt = 300 * 0.0625 ending amt = 18.75

10 months ago
OpenStudy (yuii):

Thank you both.

10 months ago
OpenStudy (wolf1728):

u r welcome

10 months ago
OpenStudy (yuii):

I wish I could medal both of you, though.

10 months ago
OpenStudy (irishboy123):

meddle the wolf!!!!!

10 months ago
OpenStudy (wolf1728):

I guess we're both good at this exponential growth / decay stuff,huh?

10 months ago
OpenStudy (irishboy123):

nah @Yuii fan up :)

10 months ago
OpenStudy (wolf1728):

LOL IrishBoy

10 months ago