The half-life of iodine-123 is about 13 hours. You begin with 52 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 ⋅ b t . Round your answer for b to three decimal places.
the complete question is The half-life of iodine-123 is about 13 hours. You begin with 52 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 ⋅ b^ t . (b) what percentage of iodine-123 remains in a sample after 36 hours? Round your answer for b to three decimal places.
Part a) we know that exponent equation formula would be an= a0( 1+r)^tand In this question, the radio isotopes will become half of its weight after the half-life. So the ratio would be -0.5 (r= -0.5)The halftime is 13 hours, so the time will be divided by that number an= a0( 1+r)^t an= a0( 1-0.5)^(t/13) an= a0( 1/2)^(t/13) a0=52 gr then an= 52( 1/2)^(t/13)
the answer part A) is an= 52( 1/2)^(t/13)
Part B) for t=36 hours
an= 52( 1/2)^(36/13)-----------> an= 52( 1/2)^(2.769)=52*(0.147) this calculation says is that after 36 hours only 0.147 of the initial mass is left
0.147---------> 14.7% of the initial mass (52 gr) is left
the answer part B) is after 36 hours remains the 14.7% of the initial mass
