Math Problem Statement
Solution
The given function for the plutonium decay is:
The problem asks for the initial amount of plutonium present, which is the value of when .
Substitute into the function:
Since , the expression simplifies to:
Thus, the initial amount of plutonium present is:
Would you like me to explain the decay function further or clarify any steps? Here are some related questions for practice:
- How much plutonium is left after 10 years?
- What does the decay constant (-0.052) represent in this function?
- How long will it take for the plutonium to decay to half of its initial value (half-life)?
- What is the value of when years?
- How would the function change if the initial amount were 5 grams instead of 3 grams?
Tip: Exponential decay functions are common in radioactive decay, population studies, and financial depreciation problems.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Radioactive Decay
Initial Value
Formulas
A(t) = A_0 * e^(-kt)
Theorems
Properties of Exponential Functions
Exponential Decay Models
Suitable Grade Level
Grades 9-12
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