Question

A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 15 hours, 55 mg of the substance remains.

How many milligrams will remain after 25 hours?

mg

Give your answer accurate to at least one decimal place.

Answer 1

We can use the formula for exponential decay:

N(t) = N0 * e^(-kt)

where:

N(t) = amount remaining after time t

N0 = initial amount

k = decay constant

We can solve for k using the given information:

55 = 110 * e^(-k * 15)

e^(-k * 15) = 0.5

-k * 15 = ln(0.5)

k = -ln(0.5) / 15

k ≈ 0.0462

Now we can use this value of k to find N(25):

N(25) = 110 * e^(-0.0462 * 25)

N(25) ≈ 39.6 mg

Therefore, approximately 39.6 milligrams will remain after 25 hours.