A sample of polonium-210 has an initial mass of 321 milligrams (mg). If the half-life of polonium-210 is 138 days, how many mg of the sample remains after 1000 hours?

Hey there!

A half-life means after a certain amount of time, half of that substance will have decayed after that time.

An equation for exponential decay is the following:

y = a(1 - b)ⁿ

Where a is the original amount, b is the rate of decay, and n is time.

1000 is about 0.3 of a half life, 1000 divided by 138 days (3312 hours) is approximately 0.3.

Let's plug in values to that equation:

y = 321(1 - 0.5)^(0.3)

Simplify.

y = 260.73

There will be 260.73mg of polonium-210 remaining after 1000 hours.

Hope this helps!