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=(ln\ 0.125)/(3)=-0.693`
The required model is:

`A=A _(0) e^(-0.693t)`