Problem
A certain drug is effective in treating a disease if the concentration remains above 100 mg/L. The initial concentration is 640 mg/L. It is known from laboratory experiments that the drug decays at the rate of 20% of the amount present each hour.
a. Formulate a model representing the concentration at each hour.
b. Build a table of values and determine when the concentration reaches 100 mg/L.
Step-by-step solution
Step 1 of 6
Consider the statement,
The description about a certain drug being effective in treating a disease and has an initial concentration
and the drug decays at the rate 
of the amount present each hour.Let
be the concentration of drug at 
hours.The initial concentration of the drug is
.Since the drug decays at the rate of 20% of the amount present each hour, the linear discrete model is given by,
Negative sign because it is decaying
Therefore,
Then,
Comment Step 2 of 6
To estimate the minimum hours at which the concentration level of the drug can be maintained above
is computed by substituting 
That is,
Since the initial concentration is 
Hence,
Comment Step 3 of 6
Substitute
in the equation 
.
Substitute
in the above equation,
Comment Step 4 of 6
Substitute
in the equation 
.Hence,
Substitute
in the above equation,
Substitute
in the equation 
.Hence,
Substitute
in the above equation,
Comment Step 5 of 6
Substitute
in the equation 
.Hence,
Substitute
in the above equation,
Substitute
in the equation 
.Hence, we get
Substitute
in the above equation,
Comment Step 6 of 6
Substitute
in the equation 
.Hence,
Substitute
in the above equation,
Substitute
in the equation 
.Hence,
Substitute
in the above equation,
Hence, after 9 hours the concentration reaches
.The behavior of the concentration of drugs with respect to time in hours is shown below:
Comment
