# Answer in Calculus for Rica #209466

The half-life of a radioactive substance is defined to be the amount of time it takes for the substance to decay 50% of its amount. If substance X has a half-life of 3,600 years, what part of substance X will remain after 4,500 years?

We know that ,

“A(t)=A_0 (frac{1}{2})^{frac{t}{T}}”

Where ,

“A_0=” the amount initially present .

“T=” the half life of the substance .

“t=” the time period over which the substance is studied .

“A(t)=” the amount of the substance present after time t .

In our case we have ,

“A_0=X, T=3600 and t=4500”

We have to calculate “A(t)=?”

Therefore according to question ,

“A(t)=X u00d7(frac{1}{2})^{frac{4500}{3600}}”

“implies A(t)=Xu00d7(frac{1}{2})^{frac{5}{4}}”

“implies A(t)=Xu00d7(0.5)^frac{5}{4}”

“implies A(t)approx Xu00d7(0.420448208)”

Hence after 4500 years approximately 0.420448208 parts of the substance remain .

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