A patient receives a 150-mg injection of a drug every 4 hours. The graph shows t

Question

A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount f(t) of the drug in the bloodstream after t hours.

Find

Explanation / Answer

lim t --> 4- = 75 lim t --> 4+ = 225 The - indicates the t-value is approaching 4 from numbers lower than 4. At t = 0 the patient gets the first injection and there is 150 mg in the blood. Over time this amount decreases as shown by the curve. At t = 4, another injection is given and the amount of medicine in the blood goes up dramatically then starts decreasing again. As the t-value approaches 4 from numbers below 4, the value of the function approaches 75. At t = 4, it looks like it is 75, until the shot is given. We don't care about the value of the function at t = 4, just what the value of the function gets closer to as t gets closer to 4. In contrast, when t approaches 4 from values higher than 4, the value of the function increases rather than decreases. As t gets closer to 4, the value of the function gets closer to something around 225. Note that at t = 4, the value of the function is not 225, it is more like 75. That does not matter, because the concern is as t approaches 4 from numbers higher than 4.

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