The half-life of sodium-24 is 14.9h. A medical facility buys a 50mg sample. How do you determine the exponential function that models the amount, A(t), of sodium-24 that will be present in the sample after t hours?
2 Answers
Explanation:
We need to find an equation of the form:
Where:
From the given information. If the half life is
Plugging this into our equation:
Dividing both sides by
Taking natural logs of both sides:
By the laws of logarithms:
So:
Exploiting the laws of indices:
Check:
Note:
If you leave this with
The function is
Explanation:
The equation for the radioactive decay is
The half life of
The initial mass is
Therefore,
graph{50e^(-0.0465x) [-11.27, 61.8, -0.3, 36.22]}