Question

The formula D=25e −0.1h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered. When the number of milligrams reaches 4 , the drug is to be administered again. What is the time between injections? The time between injections is: 9.17 hours 30.45 hours 18.33 hours 46.05 hours

Answer 1

To find the time between injections, set D equal to 4 in the formula D = 25e^(-0.1h) and solve for h. The time between injections is approximately 9.17 hours.

Step-by-step explanation:

To find the time between injections, we need to find the value of h when the number of milligrams D reaches 4. We can do this by setting D equal to 4 in the formula D = 25e^(-0.1h) and solving for h.

4 = 25e^(-0.1h)

Divide both sides by 25:

0.16 = e^(-0.1h)

Take the natural logarithm of both sides:

ln(0.16) = -0.1h

Divide both sides by -0.1:

h = ln(0.16)/-0.1

Using a calculator, we find h ≈ 9.17 hours. Therefore, the time between injections is approximately 9.17 hours.

Answer 2

The time between injections is approximately 18.33 hours.

Step-by-step explanation:

The formula D = 25e -0.1h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered.

To find the time between injections, we need to find the value of h when the number of milligrams D reaches 4.

So, we can set up the equation 4 = 25e -0.1h.

To solve for h, we can take the natural logarithm (ln) of both sides of the equation and isolate h.

ln(4/25) = -0.1h

h ≈ 18.331 hours