Question

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?

Answer 1

you know if \(t=9\) you have half of what you started with
set
\[e^{9k}=.5\] and solve for \(k\)

Answer 2

you got this? solve in two steps only

Answer 3

how do you solve for k?

Answer 4

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

Answer 5

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

Answer 6

then if you want a decimal, use a calculator

Answer 7

i have no idea what that means haha. so is it:

k= .1831?

Answer 8

no

Answer 9

wait is ln the button on the calculator for e?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

so the rate is

k= -7.7 x 10 ^-2