Question

a scientist begins with 100 mg of radioactive substance. after 6 days, it has decayed 60 mg. how long after the process began will it take to decay to 10mg

Answer 1

ok... so its exponential decay..?

Answer 2

\[A = A_{0}e^{-kt}\]

A is the current size, Ao is the initial, k is the decay constant and t = time..

Answer 3

so the 1st step is to find the decay constant

A = 60, Ao = 100 and t = 6

\[60 = 100 \times e^{-6k}\]

you need to solve for k...

before doing part 2.

Answer 4

so how do u solve for k

Answer 5

ok so divide both sides by 100

\[0.6 = e^{-6k}\]

take the base e log of both sides of the equation

\[\ln(0.6) = -6k\]

that should help you to find k.

the 2nd part asks you to find t when A = 10...

so a similar process

Answer 6

would i take the ln of both sides or just 0.6

Answer 7

yes because

\[\ln(e^a) = a\]

Answer 8

woiuld k be=0.085

Answer 9

yep... you may need to go to around 4 or 5 decimal places as it will affect the answer in the next part.

so same process to find t when A = 10

Answer 10

what do u mean A? whats formula

Answer 11

ok... so you will have

\[10 = 100 e^{-0.085138t}\]

Answer 12

now solve for t... similar process to the previous part.

Answer 13

t=-27.047

Answer 14

time can't be negative..

Answer 15

I think you'll find its a positive value

Answer 16

i keep getting a negative answer:
10=100e^-0.085138t
i dont know how to solve it

Answer 17

ln(0.1) = -0.08513t

t = ln(0.1)/-0.8513

will give a positive since the ln(0.1) is a negative