Calculating Time for Iodine 131 to Decay to 5% of Initial Dose

In summary, the conversation discusses a graph representing iodine 131 with the y-axis representing the percentage of iodine remaining in the body and the x-axis representing time in days. The equation of the graph is D = D0 (b) t/k and the value of k is 8 for the iodine half-life. The question is then asked to determine how many days will have passed until the dose of iodine 131 is undetectable using the equation D(t)=D_02^{-\frac{t}{8}}. It is suggested to set D(t)=0.05D_0 and solve for t to find the answer.
  • #1
Pikachu1
8
0
So i have a graph representing iodine 131
y axis of 0-100 iodine remaining in the body (%of dose)
x asis 0-60 Time in days
with the points plotted (24,12.5)

The equation of the graph is D = D0 (b) t/k

So i have figured out "k" which is 8 for iodine half life. Which it asked me to do in the previous question.

Now it is asking me...

Iodine 131 is unable to be detected after it has decayed to 5% of its initial dose. Using your equation, determine how many days, to the nearest tenth will have passed until the dose is undetectable.

Just not sure how to use my equation to get that answer. I realize it's simple but it is out smarting me.
 
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  • #2
Okay the curve is:

\(\displaystyle D(t)=D_02^{-\frac{t}{8}}\)

To find the time at which the initial dose has decayed to 5% of the original amount, you may set $D(t)=0.05D_0$ and then solve for $t$. Can you proceed?
 

Related to Calculating Time for Iodine 131 to Decay to 5% of Initial Dose

What is exponential decay?

Exponential decay is a mathematical concept that describes the decrease of a quantity over time in a specific pattern. It occurs when a quantity is reduced by a constant percentage at regular intervals.

What is the formula for exponential decay?

The formula for exponential decay is y = abx, where "y" is the final amount, "a" is the initial amount, "b" is the decay factor, and "x" is the number of time intervals.

How do I calculate the decay factor in exponential decay?

The decay factor in exponential decay is calculated by taking the ratio of the final amount to the initial amount and raising it to the power of 1 over the number of time intervals. In other words, b = (y/a)1/x.

What is the half-life in exponential decay?

The half-life in exponential decay is the amount of time it takes for the initial quantity to decrease by half. It is represented by the symbol "t1/2" and can be calculated using the formula t1/2 = ln(2)/k, where "k" is the decay rate.

How is exponential decay used in science?

Exponential decay is used in many scientific fields, such as nuclear physics, biology, and chemistry. It can be used to model the decay of radioactive substances, the growth and decay of populations, and the degradation of natural resources, among other applications.

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