Question

A radioactive substance decays exponentially. A scientist begins with 350 milligrams of a radioactive substance. After 14 hours, 175 mg of the substance remains. How many milligrams will remain after 20 hours

Answer 1

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Explanation:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Answer 2

≈ 130 mg

Explanation:

This is about the half-life of the substance.

There is a formula for this kind of calculations:

N(t)= N₀*(0.5)^(t/T), where

• N(t) = substance left after time period of t,
• t = time passed,
• N₀ = initial amount of the substance,
• T = hal-life time of the given substance.

In our case, we have:

• N₀ = 350 mg,
• t= 20 hours,
• T = 14 hours as half of substance decays during this time period,

And the calculation:

• N(20)= 350*(0.5)^(20/14)
• N(20) ≈ 130 mg

Answer: about 130 mg of substance remains after 20 hours