a radioactive material is undergoing nuclear decay. After 40 minutes, 25% of the sample remains. What is the half-life of the sample

This is the long way but I would do this.

ln(No/N) = kt
Substitute
No = 100 (just make up any number)
N = 25 (25% of whatever you picked for No)
k = solve for this
t = 40 minutes.

Then substitute k into
k = 0.693/t1/2 and solve for t1/2.

To find the half-life of the radioactive material, we can use the information given: after 40 minutes, 25% of the sample remains.

The half-life of a radioactive substance is the time it takes for half of the substance to decay or disintegrate. In this case, after the half-life, only 50% (half) of the sample will remain.

Since we are given that after 40 minutes, 25% (or 25/100) of the sample remains, we can set up the following equation:

(1/2) = (25/100) * (1/x)

Where x represents the time in minutes for the half-life of the radioactive material.

To solve for x, we can simplify the equation:

1/2 = 1/4 * (1/x) [Multiplying both sides of the equation by 4]

1/2 = 1/x

Next, we can cross-multiply and solve for x:

2 * x = 1 [Multiplying both sides of the equation by x]

2x = 1

Divide both sides by 2:

x = 1/2

Therefore, the half-life of the sample is 0.5 (or 1/2) minutes.