Answer :
Algebraically the amount of Cs-137 remaining will drop below 1 kg approximately 460.516 years after 1986. To find when the amount of Cs-137 remaining will drop below 1 kg, we need to solve the equation y = 1000(0.50)ˣ/³⁰ for x when y < 1.
We can rewrite the equation as 0.001 = (0.50)ˣ/³⁰ by dividing both sides by 1000. To solve for x, we can take the logarithm of both sides. Applying the logarithm base 0.50 to both sides, we get log₀.₅₀(0.001) = x/³⁰. Simplifying further, we have log₀.₅₀(0.001) = x/30.
Using the change of base formula, we can rewrite the equation as log(0.001)/log(0.50) = x/30. Evaluating the left side of the equation, we find that x ≈ -460.516.
The amount of Cs-137 remaining will drop below 1 kg approximately 460.516 years after 1986.
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