Calculus
posted by Molly .
24. A pharmaceutical company has determined that a realistic model for the relationship between blood pressure (systolic) and the amount of a nerve drug designed to reduce the systolic pressure is given by the equation P=Pi + 2x  x^2.
P is measured in millimeters of mercury and x is the number of milligrams of the drug administered 30 minutes before the reading of the pressure P. Pi is the systolic pressure before the medicine is taken and will vary with each patient. However, Pi must fall in the range 200 less than or equal to Pi greater than or equal to 220, for the model to be valid.
a. Determine the rate of change of the systolic pressure P with respect to the amount of drug, x, administered.
b. Determine the minimum amount of the drug that can be administered and still be effective.
c. If a particular patient has an initial systolic pressure of 200 and 10 milligrams of the drug administered, what will the pressure be 30 minutes later?
Note:
For part a. the answer is 22x. Is this because Pi is considered a number between 200 and 220 and the equation P=Pi + 2x  x^2 is then used to find the derivative.

a. dP/dx = 2  2x
b. In order for dP/dx to be negative (and the drug to therefore be effective, x must be >1 mg.
c. If x = 10 and Pi = 200, then P = Pi + 2x  2x^2 after 30 minutes
= 200 +20 200 = 20 mm mercury
Sounds like an overdose to me
Respond to this Question
Similar Questions

Statistics
Suppose we have a set of blood pressures with a mean of 120 Systolic, and a sample standard deviation of 20 points. If we assume a normal distribution of Systolic blood pressures, then between what two values can we be assured 99.7% … 
statistics
Suppose we have a set of blood pressures with a mean of 110 Systolic, and a sample standard deviation of 15 points. If we assume a normal distribution of Systolic blood pressures, then between what two values can we be assured 99.7% … 
Statistic
In a population of over 15,000 patients, the distribution of systolic blood pressure follows the normal curve. Investigators believe the average systolic blood pressure in the population is 120 mm. The investigators take a simple random … 
Statistics
Jim's systolic blood pressure is a random variable with a mean of 145 mmHg and a standard deviation of 20 mmHg. For Jim's age group, 140 is the cutoff for high blood pressure. If Jim's systolic blood pressure is taken at a randomly … 
calculus 1
Suppose that a personâ€™s blood pressure at time t in seconds is given by p(t) = 100 + 18 sin (7t). (a) During each heartbeat, what is the systolic pressure (maximum blood pressure) and the diastolic pressure (minimum blood pressure)? 
Math
The systolic blood pressures of a group of 18yearold women are normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of women in this group have a systolic blood pressure between 108 mmHg … 
math
A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After … 
statistic
A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After … 
physic
If an erect person's systolic pressure is measured at 120 mmHg at the level of heart, please calculate the arterial systolic blood pressure in the head of this person (in the unit of mmHg). Assume that the head is 50 cm above the … 
Stats need help
Use the empirical rule to solve the problem. The systolic blood pressure of 18 yr. old women is normally distributed with a mean of 120 mmHg (millimeters of Mercury) and a standard deviation of 14 mmHg. What is the percentage of 18 …