The sensitivity S to a drug is related to the dosage size by , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity.
A) Milliliters, Milliliters
B) Milliliters, Milliliters
C) Milliliters, Milliliters
D) Milliliters, Milliliters
E) Milliliters

Question

The sensitivity S to a drug is related to the dosage size by  , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. ​
A) Milliliters, Milliliters 
B) Milliliters, Milliliters 
C) Milliliters, Milliliters 
D) Milliliters, Milliliters 
E) Milliliters

Quizplus · Accepted Answer

To find the dosage that yields 0 sensitivity, we need to solve the equation S(x) = 0, where S(x) = 11eb0d3b_97a5_0ddc_9790_334e7c7bca3a_TB1243_11.

Substitute S(x) with 0:

0 = 11eb0d3b_97a5_0ddc_9790_334e7c7bca3a_TB1243_11

Take the natural logarithm of both sides:

ln 0 = ln(11eb0d3b_97a5_0ddc_9790_334e7c7bca3a_TB1243_11)

This is undefined since ln(0) is undefined. Therefore, there is no dosage that yields 0 sensitivity.

However, if we take the limit as x approaches negative infinity, we can see that S(x) approaches 0. Therefore, the smallest dose of the drug (in the negative direction) would yield the closest approximation to 0 sensitivity.

Using a calculator or a graphing tool, we can see that the limit of S(x) as x approaches negative infinity is 0. This occurs at x = 11eb0d3b_97a5_34ef_9790_17d9b7579d6e_TB1243_11 milliliters.

Therefore, the answer is choice B.

The Sensitivity S to a Drug Is Related to the Dosage