How much of a radioactive substance must be presented to decay to 60 grams in 11 years if the half-life of the substance is 3.9 years?
Select one:
a. Between 400 and 420 grams
b. Between 420 and 440 grams
c. Between 440 and 460 grams
d. Over 460 grams
x * (1/2)^(11/3.9) = 60
now just solve for x
To solve this problem, we need to use the formula for exponential decay:
N = N₀ * (1/2)^(t/t₁/₂)
Where:
N is the final amount of the substance,
N₀ is the initial amount of the substance,
t is the total time passed,
t₁/₂ is the half-life of the substance.
In this case, we know that the initial amount (N₀) is the amount we need to find and is represented by the variable x. The final amount (N) is given as 60 grams, the total time (t) is 11 years, and the half-life (t₁/₂) is 3.9 years.
Plugging these values into the formula, we have:
60 = x * (1/2)^(11/3.9)
To find x, we can rearrange the equation:
x = 60 / (1/2)^(11/3.9)
Using a calculator, we can evaluate this expression and find that x is approximately 440 grams.
Therefore, the correct answer is:
c. Between 440 and 460 grams