The amount of Mineral x left in the bloodstream can be calculated using the exponential decay formula which is y = a * (r^t).
Here:
- 'y' is the amount of material left.
- 'a' is the initial amount of the material.
- 'r' is the decay rate.
- 't' is the time that has passed.
Given in the question,
- The initial amount 'a' is 500 milligrams.
- The decay rate 'r' is 0.06 per hour.
- The time 't' is 3 hours.
First, we substitute these values into our formula.
We have y = 500 * (0.06^3).
Next, we perform the calculations on the right-hand side.
First, we calculate the third power of 0.06, which is 0.06^3 = 0.000216.
Then, we multiply this by the initial amount 500, which gives us 500 * 0.000216 = 0.108 milligrams.
So, after 3 hours, approximately 0.108 milligrams of Mineral x are left in the bloodstream.