(Solved): Assignment 21A All Questions 1 and 2   Recall that half-life refers to the amount of time ...

Assignment 21A
All Questions 1 and 2

 

Recall that half-life refers to the amount of time it takes for a quantity to decrease to half of its original value. 1) Acetaminophen has a half-life of approximately 4 hours. Suppose that a person takes a single 500-milligram dose. Part A: Write a formula for \( f(t) \), where \( f(t) \) is the amount of acetaminophen in a person's bloodstream after \( t \) 4-hour periods have elapsed. Hint: Remember that \( t \) is not measured in hours; instead, \( t \) counts the number of 4 hour periods. Part B: Write a formula for \( g(n) \), where \( g(n) \) is the amount of acetaminophen in a person's bloodstream after \( n \) hours have elapsed. Hint: Recall that \( t=4 n \), where \( n \) is hours. Part C: If one were to construct a graph of the function \( g \), where would the vertical intercept be? Hint: What is the value of the function when \( n=0 \) ? 2) Suppose that the amount of a drug in milligrams in a person's body after \( n \) hours is given by the equation \[ f(n)=325\left(\frac{1}{2}\right)^{n / 9} \] Part A: What is the half-life of the drug? Hint: Examine the exponent in the formula given. What value of \( n \) would be necessary in order for the formula to produce \( 325\left(\frac{1}{2}\right) \) ? Part B: How much of the drug did the person take initially? Hint: Think about how the original dose is related to the equation.