After a spill of radioactive iodine, measurements showed the ambient radiation levels at the site of the spill to be four times the maximum acceptable limit. The level of radiation from an iodine source decreases according to the formula: R(t)=Re^-0.004t where R is the radiation level (in millirems/hour) at time t in hours and R is the initial radiation level (at t=0).
a) How long will it take for the site to reach an acceptable level of radiation?
b) How much total radiation (in millirems) will have been emitted by that time, assuming the maximum acceptable limit is 0.6 millirems/hour?

Question

After a spill of radioactive iodine, measurements showed the ambient radiation levels at the site of the spill to be four times the maximum acceptable limit. The level of radiation from an iodine source decreases according to the formula: R(t)=Re^-0.004t where R is the radiation level (in millirems/hour) at time t in hours and R is the initial radiation level (at t=0). 
a) How long will it take for the site to reach an acceptable level of radiation?
b) How much total radiation (in millirems) will have been emitted by that time, assuming the maximum acceptable limit is 0.6 millirems/hour?

dumbcow · Answer

so the initial level "R" is 4 times the max limit
Let R = 4L, find t such that R(t) = L
$$4Le^{-.004t} = L \rightarrow e^{-.004t} = \frac{1}{4}$$
take log of both sides
$$-.004t = \ln (1/4)$$
$$t = 346.57$$

dumbcow · Answer

for next part, to find the amount of radiation you have to integrate over R(t) from 0 to 346.57
L = 0.6 --> R = 2.4
$$2.4\int\limits_{0}^{346.57}e^{-.004t} dt$$

anonymous · Answer

Thank you. :)

dumbcow · Answer

welcome