The half-life of iodine-123 is about 13 hours. You begin with 38 grams of iodine-123.

(a) Write an equation that gives the amount of iodine-123, I, remaining after t hours. Write your answer in the form I (t) = a⋅bt.

(b) Determine the number of hours needed for your sample to decay to 7 grams. Round your answer to the nearest integer

Half-life, h = 13 hours

Mass initial, a = 38 g

B=base for half-life = 2

(a)

I (t) = a*B^ (-t/h) = a * (B^ (1/h) ^ (-t) = a * (B^ (-1/13)) ^t

Substituting values,

I (t) = 38 * (2^ (-1/13)) ^t

a=38 g

b=2^ (-1/13) = 0.9480775 (approximately)

=>

I (t) = 38*0.9480775^t

(b) I (t) = 7

solve

I (t) = 7=38*0.948077^t

Take log on both sides and solve for t

t=log (7/38) / log (0.948077)

=31.727 hours.

Check: I (31.727) = 38*9.948077^ (31.727) = 7.000 g ok