Question

A radioactive substance decays at a rate of y = ae^-0.1483t, where t is in hours. Find the half-life of the substance.

t = 0.8622 years
t = 4.674 years
t = 18.323 years
t = 0.1028 years

Answer 1

The half-life of the radioactive substance is approximately 4.677 hours.

Step-by-step explanation:

To find the half-life of the radioactive substance, we need to set the value of y equal to half of the initial amount of the substance and solve for t.

Given the decay rate function y = ae^-0.1483t, where t is in hours, we can set y = 0.5 to represent half of the initial amount.

0.5 = ae^-0.1483t

Now, we can solve for t by taking the natural logarithm of both sides.

ln(0.5) = -0.1483t

Dividing both sides by -0.1483 gives us:

t = ln(0.5) / -0.1483 ≈ 4.677 hours

Therefore, the half-life of the substance is approximately 4.677 hours.