A radioactive substance decays exponentially.If 700 grams were present initially and 300 grams are present 100 years later,how many grams will be present after 400 years? Round your answer to two decimal places,if necessary.
A)22.37 grams
B)21.12 grams
C)0)00 grams
D)23.62 grams

Question

Quizplus · Accepted Answer

We can use the formula for exponential decay:

N(t) = N₀e^(-kt)

where N(t) is the amount of substance remaining after t years, N₀ is the initial amount, k is the decay constant, and e is the mathematical constant.

We can solve for k first by using the fact that 300 grams are present after 100 years:

300 = 700e^(-k*100)
e^(-10k/7) = 3/7
-10k/7 = ln(3/7)
k = -7/10 * ln(3/7)

Now we can use this value of k to find the amount remaining after 400 years:

N(400) = 700e^(-(-7/10*ln(3/7))*400)
N(400) ≈ 23.62 grams

Therefore, the best choice is D.

A Radioactive Substance Decays Exponentially