Posted by **Anonymous** on Sunday, January 27, 2013 at 4:36pm.

The half life of a certain radioactive substance is 10 years. How long will it take for 18 gms of the substance to decay to 6 gms?

A. 6 ln 10 years

B. 10 ln 6 years

C. 10 (ln 3)/(ln 6) years

D. 18 ln 10 years

E. 10 (ln 3)/(ln 2) years

- Calculus -
**Damon**, Sunday, January 27, 2013 at 4:50pm
.5 = e^-k(10)

-.693 = -10 k

k = .0693

then

6/18 = e^-.0693 t

-1.0986 = - .0693 t

t = 15.9 years

- Calculus -
**Reiny**, Sunday, January 27, 2013 at 4:50pm
I would solve

18(1/2)^(t/10) = 6

(1/2)^(t/10) = 1/3

from the answers, my clue would be to take ln of both sides

- Calculus -
**Anonymous**, Sunday, January 27, 2013 at 5:07pm
Thanks I think it would be E.10 (ln3)/(ln2) years

Right?

- Calculus -
**Damon**, Sunday, January 27, 2013 at 5:21pm
10 ln 3/ln 2 = 15.9 yes

- Calculus -
**Austin**, Sunday, January 27, 2013 at 9:52pm
P = P(0)e^(kt)

(1/2) = e^(10k)

ln(1/2) = 10k

k = (1/10)ln(1/2)

----------------

6 = 18e^((1/10)ln(1/2)t)

(1/3) = e^((1/10)ln(1/2)t)

t = 10[ln(1/3)/ln(1/2)]

t = 10[-ln(3)/-ln(2)]

t = 10[ln(3)/ln(2)]

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