Question

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101.
Find the substance's half-life, in days. Round your answer to the nearest tenth.

Answer 1

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

What is the formula for half-life?

Exponential decay obeys the equation

$m(t) = m_0 e^{-kt}$

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

$m(t) = m_0 e^{-kt}$

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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