question

Quote:

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

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:

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

Now plug in all known values and solve for t:

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