Question

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 7%. If the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (Round your answer to one decimal place.)

Answer 1

To find the amount remaining after 24 hours, you can use the formula for exponential decay of radioactive nuclei: R = R0 *e^-kt, where R is the amount remaining after time t, R0 is the initial amount, k is the rate constant, and t is the time. By calculating the rate constant and plugging in the values, the amount remaining after 24 hours is approximately 57.7 milligrams.

Step-by-step explanation:

To find the amount remaining after 24 hours, we can use the formula for exponential decay of radioactive nuclei:

R = R0 * e-kt

where R is the amount remaining after time t, R0 is the initial amount, k is the rate constant, and t is the time. In this case, the rate of decay is proportional to the amount of the substance present, so we can find the rate constant by taking the natural logarithm of 1 - 7% (0.93) and dividing it by 6 hours:

k = ln(0.93) / 6

Now we can plug in the values into the formula to find the amount remaining after 24 hours:

R = 100 * e-k * 24

Calculating this, we find that approximately 57.7 milligrams of the radioactive substance remain after 24 hours.