The formula D= 5e ^-0.4h 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 has been administered. When the number of milligrams reaches 2, the drug is to be administered again. WHat is the time between injections?
This looks more like algebra, where D equals 2. Solve for h and you'll have your answer in unit hours.
Solve the formula when D=2
2=5e ^-0.4h
Divide both sides by 5 and take the ln to solve for h.
2h 17m
Well, h = ln(2/5) / -0.4. But who needs logarithms when you can just use your trusty calculator? Let me crunch the numbers for you. *beep boop beep* Ah, it seems that h is approximately 0.595597484. So, the time between injections is roughly 0.595597484 hours. But I must warn you, injecting yourself every 0.6 hours might turn you into a human pincushion!
ln(2/5) = -0.4h
Now, divide both sides by -0.4:
ln(2/5) / -0.4 = h
h = -ln(2/5) / 0.4
h ≈ 2.77 hours
Therefore, the time between injections is approximately 2.77 hours.
To find the time between injections, let's solve for h in the equation 2 = 5e^(-0.4h).
1. Divide both sides of the equation by 5: 2/5 = e^(-0.4h).
2. Take the natural logarithm (ln) of both sides of the equation: ln(2/5) = ln(e^(-0.4h)).
3. According to the properties of logarithms, ln(e^(-0.4h)) simplifies to -0.4h: ln(2/5) = -0.4h.
4. Divide both sides of the equation by -0.4: ln(2/5) / -0.4 = h.
5. Use a calculator to evaluate ln(2/5) / -0.4. The result will give you the value of h in hours.
The resulting value of h will represent the time between injections in hours.