Exponential Decay/and growth question involving half life.

**A 200 gram sample of compound XYZ has a half life of 304 hours.**

a.) state the decay/growth factor.

b.) write an exponential equation that models this scenario.

c.) Calculate how many grams of the sample will be left after 60 days to the nearest 100th of a gram.

Please solve and explain. I have a quiz on this tomorrow.

Re: Exponential Decay/and growth question involving half life.

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Originally Posted by

**Nabilrahman16** **A 200 gram sample of compound XYZ has a half life of 304 hours.**

a.) state the decay/growth factor.

b.) write an exponential equation that models this scenario.

c.) Calculate how many grams of the sample will be left after 60 days to the nearest 100th of a gram.

Please solve and explain. I have a quiz on this tomorrow.

two ways to go about this (y in grams, t in days) ...

$\displaystyle y = 200\left(\frac{1}{2}\right)^{k_1 \cdot t}$

$\displaystyle 100 = 200\left(\frac{1}{2}\right)^{k_1 \cdot \frac{38}{3}}$

solve for $\displaystyle k_1$ and you have your decay function.

or ...

$\displaystyle y = 200e^{k_2 \cdot t}$

$\displaystyle 100 = 200e^{k_2 \cdot \frac{38}{3}}$

solve for $\displaystyle k_2$, same idea.