# Math Help - continuous rate problem

1. ## continuous rate problem

A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour.

a.)Write a formula for the amount of , A mg, of caffeine in the body t hours after drinking a cup of coffee.

How do i handle these type of problems?? what are the variations of this type of problem? Ex.. Half life , double half life..

2. $A = 100(.83)^t$ where t is in hours.

3. Originally Posted by VkL
If the amount of coffee is x, 17% of that is 0.17x. Where you go from there depends upon what you know. If you know Calculus, you can say that the rate of change is dx/dt so dx/dt= -0.17x. Then dx/x= -0.17dt and, integrating, ln(x)= -0.17t+ c so $x= Ce^{-.17t}$ where C is $e^c$. If the initial value of x is 100 mg, then x(0)= C= 100 so $x(t)= 100e^{-0.17t}$