Question

A scientist begins with 150 milligrams of a radioactive substance that decays exponentially. After 35 hours, 75 milligrams of the substance remains. How many milligrams will remain after 57 hours, rounded to the nearest milligram?

(A) 37.5
(B) 46.9
(C) 75
(D) 112.5

Answer 1

To find the remaining milligrams of the radioactive substance after 57 hours, use the exponential decay equation. The answer is approximately 46.9 milligrams.

Step-by-step explanation:

To determine how many milligrams of the radioactive substance remain after 57 hours, we need to solve for the decay constant in the exponential decay equation.

Using the given information, we have:

Initial amount = 150 milligrams

Remaining amount after 35 hours = 75 milligrams

Decay constant = ln(2) / half-life = ln(2) / 35

We can use this decay constant to find the remaining amount after 57 hours:

Remaining amount after 57 hours = Initial amount * e^(-decay constant * 57)

Substituting the values, we get:

Remaining amount after 57 hours = 150 * e^(-ln(2)/35 * 57)

Rounded to the nearest milligram, the answer is approximately 46.9 milligrams.