SOLUTION: I'm not entirely sure this is the right subject, sorry if it's not...
A substance decomposes radioactively. Its half-life is 32 years. Find the constant "k" in the decay formula
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Question 568663: I'm not entirely sure this is the right subject, sorry if it's not...
A substance decomposes radioactively. Its half-life is 32 years. Find the constant "k" in the decay formula.
Use this formula instead:
y= final value
n= initial value
k= constant
t= time
e= antilogarithm
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is NOT the antilogarithm. is the base of the natural logs, that is: \ =\ \log_e(x))
If one half-life has elapsed, then 
.
Since the half-life of the substance in question is 32 years, then
Take the natural log of both sides:
\ =\ \ln\left(\frac{1}{2}\right))
Use
\ =\ n\log_b(x))
to write
\ =\ \ln\left(\frac{1}{2}\right))
Use "the difference of the logs is the log of the quotient",
 - \log_b(y) = \log_b\left(\frac{x}{y}\right))
to write
\ =\ \ln(1)\ -\ \ln(2))
Use
\ =\ 1)
to write
\ -\ \ln(2))
then use
\ =\ 0)
to write
)
then
}{32}\ \approx\ -0.022)
John
My calculator said it, I believe it, that settles it
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