6.
The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.
A) y=2(1/361)1/32x; 0.797 kg
B) y=1/2(1/361)^1/32; 0.1999 kg
C) y=361(1/2)^11/32x; 323.925 kg
D) y=361(1/2)^32x; 0 kg
I think it's C, could anyone help me? Thank you!
To determine the correct exponential function that models the decay of the radioactive material, we need to start with the general form of an exponential decay function. It is given by the formula:
y = A(1/2)^(t/h)
Where:
y represents the remaining amount of material after time t
A is the initial amount of material
t is the time that has elapsed
h is the half-life of the material
Given that the half-life of the material is 32 days and the initial amount is 361 kg, we can substitute these values into the formula:
y = 361 (1/2)^(t/32)
Using this formula, we can now determine the amount of radioactive material remaining after 5 days:
y = 361 (1/2)^(5/32)
Calculating this value, we find that y is approximately 323.925 kg.
Therefore, the correct answer is option C: y = 361(1/2)^(11/32) = 323.925 kg.
To model the decay of the radioactive material, we can use the formula for exponential decay:
A(t) = A₀ * (1/2)^(t/h)
where A(t) is the amount of material remaining after time t, A₀ is the initial amount of material, and h is the half-life of the material.
In this case, the initial amount A₀ is 361 kg and the half-life h is 32 days. So the exponential decay function for this problem is:
A(t) = 361 * (1/2)^(t/32)
To find how much radioactive material remains after 5 days, we substitute t = 5 into the equation:
A(5) = 361 * (1/2)^(5/32)
Calculating this, we find that A(5) is approximately 323.925 kg.
So the correct answer is C) y = 361(1/2)^(11/32)x, 323.925 kg.