Question

In a hospital, a patient was administered 300 milligrams of saline. the function below can be used to determine the amount of saline in the patient’s bloodstream after h hours. f(h)=300(12)h/2.5 f ( h ) = 300 ( 1 2 ) h / 2.5 how many milligrams of saline are present in the patient’s blood after 5 hours? responses 2 mg 2 mg 75 mg 75 mg 150 mg 150 mg 300 mg

Answer 1

After 5 hours, there are 75 milligrams of saline present in the patient's bloodstream, calculated by evaluating the decay function f(h) = 300(1/2)^(h/2.5) at h = 5.

Step-by-step explanation:

The student is asking how many milligrams of saline are present in a patient's blood after 5 hours, given the function f(h) = 300(1/2)^(h/2.5) to model the decay of saline in the bloodstream over time. To find the answer, we must plug h = 5 into the equation and solve for f(5).

Step 1: Substitute h with 5 into the equation:

f(5) = 300(1/2)^(5/2.5)

Step 2: Simplify the exponent:

5 / 2.5 = 2

Step 3: Now raise (1/2) to the power of 2:

(1/2)^2 = 1/4

Step 4: Multiply 300 by 1/4:

300 * 1/4 = 75 mg

Therefore, after 5 hours, there are 75 milligrams of saline present in the patient's bloodstream.