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openstudyhelpplease Group Title 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? one year ago one year ago

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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

3. openstudyhelpplease

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

7. openstudyhelpplease

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

8. satellite73

no

9. openstudyhelpplease

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

11. openstudyhelpplease

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

12. openstudyhelpplease

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

13. openstudyhelpplease

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