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Estimating Half Life Computations

The half life of carbon is 5,730 years. What percentage of the carbon is left if the original carbon has been present for 35,000 years?

half-life: 100% → 50% → 25% → 12.5% → 6.25% → 3.125% → 1.5625%

$A=A_{0}(\frac{1}{2})^{\frac{t}{h}}$

$A=A_{0}(\frac{1}{2})^{x}$

$A=A_{0}(\frac{1}{2})^{\frac{35,000\ years}{5,730\ years}}$

$\frac{A}{A_{0}}=(\frac{1}{2})^{\frac{35,000}{5,730}}$

$\frac{A}{A_{0}}\approx (\frac{1}{2})^{6}$ ← estimate

About 1.5% of the original carbon left

$\frac{A}{A_{0}}=(\frac{1}{2})^{\frac{35,000}{5,730}}$

$\frac{A}{A_{0}}=1.45\%$