Final answer:
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.