## openstudyhelpplease 2 years ago A certain radioactive element decays according to N=No e ^-kt. If 50% of the original element sample remains after 9 days, what is the decay rate?

1. satellite73

you know if $$t=9$$ you have half of what you started with set $e^{9k}=.5$ and solve for $$k$$

2. satellite73

you got this? solve in two steps only

how do you solve for k?

4. satellite73

1) write in equivalent logarithmic form (take the log) 2) divide by 9

5. satellite73

$e^{9k}=.5\iff 9k=\ln(.5)\iff k=\frac{\ln(.5)}{9}$

6. satellite73

then if you want a decimal, use a calculator

i have no idea what that means haha. so is it: k= .1831?

8. satellite73

no

wait is ln the button on the calculator for e?

10. satellite73

http://www.wolframalpha.com/input/?i=ln%28.5%29%2F9 usually $$ln$$ is the button and $$e$$ requires the shift key

ok, so i have to use the shift key right? i tried doing e ^.5 which was 1.64 and then divide that by 9 which was .1831

oh, the link helped. sorry we didn't learn this yet so I have no idea what im talking about

so the rate is k= -7.7 x 10 ^-2

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