A element emits radiation and he started with .07 grams. After 5 days only .05 of the original element remain. Use the formula A(t)=Aoe^kt

Question

A.Calculate the value of K.

B.Find the half life

Would love some help on this as i can't find the solution anywhere.

Answer 1

A(t) = A_oe^kt

A(t) = 0.05

Ao = 0.07

t = 5 days

k = ?

0.05 = 0.07e^5k

0.05/0.07 = e^5k

Take ln of both sides: ln (0.05/0.07) = 5k

-0.3365 = 5k

k = -0.06729

Once you have k, you can solve fo half life:

Set A(t) = 1/2 A_o

1/2 A_o = A_oe^-0.06729t

1/2 = ^e-0.06729t

-0.6931 = 0.06729t

t = 10.3 days = half life