question

the dissolution of a tablet in a stomach is described by the following model: y=Ae(-Bt)
y=weight of a tablet in grams
t=time in minutes
when swallowed the tablet weights 30 grams. the half-life of the tablet is 12 minutes. how long does the tablet take to issolve down to 10 grams

Quote:

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Originally Posted by sarahfox

the dissolution of a tablet in a stomach is described by the following model: y=Ae(-Bt)
y=weight of a tablet in grams
t=time in minutes
when swallowed the tablet weights 30 grams. the half-life of the tablet is 12 minutes. how long does the tablet take to issolve down to 10 grams

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Hi,

to answer your question you have to calculate the value of B first:

Let A = 1 g then you know that there are 0.5 g left after 12 minutes:

$\displaystyle \frac12 = 1 \cdot e^{-B \cdot 12}~\iff~\ln\left(\frac12\right)=-B \cdot 12~\iff~B = \frac1{12} \cdot \ln(2)$

Now plug in all known values and solve for t:

$\displaystyle 10 = 30 \cdot e^{-\frac1{12} \cdot \ln(2) \cdot t}~\iff~-\ln(3)=-\frac1{12} \cdot \ln(2) \cdot t~\iff~ t = 12 \cdot \frac{\ln(3)}{\ln(2)} \approx 19.02\ min$