Question

A doctor prescribe 125 miligrams of a therapeutic drug that decays by about 10% each hour. Write an exponentia lmodel representing the amount A in milligrams of the drug remainng in the patient's system after t hours.

Answer 1

Answer:

$C(t)=125\cdot 0.9^t$

Step-by-step explanation:

Exponential Decay Function

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

$C(t)=C_o\cdot(1-r)^t$

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The doctor prescribed 125 milligrams of a therapeutic drug. It decays by 10% each hour. The initial value is Co=125 and the decay rate is r=0.1 per hour. Substituting into the function:

$C(t)=125\cdot(1-0.1)^t$

Operating:

$\mathbf{C(t)=125\cdot 0.9^t}$

Where t is expressed in hours.