Question

Soon after taking an aspirin, a patient has absorbed 320 mg of the drug. after 3 hours, only 40 mg remain. find an exponential model for the amount of aspirin in the bloodstream after t hours

Answer 1

The equation will be of the form:
$A(t)= A_{0} e^{rt}$
where A is the amount after t hours, and r is the decay constant.
To find the value of r, we plug the given values into the equation, giving:
$40=320e^{3r}$
Rearranging and taking natural logs of both sides, we get:
$ln\ 0.125=3r$
$r=\frac{ln\ 0.125}{3}=-0.693$
The required model is:
$A=A _{0} e^{-0.693t}$