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Mekhanik [1.2K]
3 years ago
5

The half-life is a substance is 375 years. If 70 grams is present now, how much will be present in 500 years?

Mathematics
1 answer:
Lynna [10]3 years ago
3 0

Answer:

27.76 grams will be present in 500 years

Step-by-step explanation:

The given formula is A=A_{o}e^{kt} , where A is the value of the substance in t years, and A_{o} is the initial value

∵ The half-life is a substance is 375 years

- Substitute A by \frac{1}{2}A_{o} and t by 375 to find the value of k

∴ \frac{1}{2}A_{o}=A_{o}e^{375k}

- Divide both sides by A_{o}

∴ \frac{1}{2}=e^{375k}

- Insert ㏑ in both sides

∴ ㏑( \frac{1}{2} ) = ㏑ ( e^{375k} )

- Remember ㏑ ( e^{n} ) = n

∵ ㏑ ( e^{375k} ) = 375 k

∴ ㏑( \frac{1}{2} ) = 375 k

- Divide both sides by 375

∴ k ≈ -0.00185

∴  A=A_{o}e^{-0.00185t}

∵ 70 grams is present now

- That means the initial value is 70 grams

∴ A_{o} = 70

∵ The time is 500 years

∴ t = 500

- Substitute the values of A_{o} and t in the formula

∵ A=70e^{-0.00185(500)}

∴ A = 27.76

∴ 27.76 grams will be present in 500 years

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