Question

who is good at half-life problems?

Answer 1

Shoot...

Answer 2

Thirty percent of a radioactive substance decays in four years. Assuming the decay is exponential, find half life of the substance.

Answer 3

I am stumped. Sorry. Need to go study this one!

Answer 4

pretty easy...where are you stuck

Answer 5

the whole problem

Answer 6

no worry's GT

Answer 7

if you start with one unit of substance , how much would you have after 4 years

Answer 8

can you answer that

Answer 9

no

Answer 10

0.7 units

Answer 11

yes..now plug that into the exponential decay model and solve for k

\[A=A_0e^{kt}\]

Answer 12

You are solving for e^kt = 1/2?

Answer 13

not yet...we have to find k first

Answer 14

\[\ln .70/4=k\]

Answer 15

good

Answer 16

-0.089

Answer 17

yes

Answer 18

now use your k and solve this for t

\[\frac{1}{2}=e^{kt}\]

Answer 19

@zarkon - thanks! I learned (rather refreshed my memories!) of it.

Answer 20

no problem

Answer 21

ln(.5)/(?)=t

Answer 22

would the -0.089 replace the ?

Answer 23

It has to.

Answer 24

yes...that is where k goes

Answer 25

7.788=t rite

Answer 26

I get 7.7734328395

Answer 27

I let the calculator keep all the digits

Answer 28

ohh okay i see now

Answer 29

The radioactive element polonium has a half-life of 140 days. If 15 mg of this substance decays exponentially, find:
A.) How much of the substance would remain after 60 days.
B.) how long would it take before it becomes 4 mg.

Answer 30

solve

\[\frac{1}{2}=e^{k\cdot140}\]
for k

Answer 31

after finding k

A) evaluate \[15e^{k\cdot 60}\]

B) solve \[4=15e^{k\cdot t}\] for t

Answer 32

okay let me try it

Answer 33

-0.004951051=k