The number of milligrams of a particular medication in a patient's body after t minutes can be modelled by the function a(t)=1/2 x cubed

Question

The poiints (2,4) and (6,108) are on the graph of a(t). Find the average rate of change between the points (2,4) and (6,108) Interpret your answer in the context of the situation.

Answer 1

The average rate of change is another way of asking for the slope, meaning we want

output 2 - output 1

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input 2 - input 1

a.k.a. rise over run. Our two points are (2,4) and (6,108), so the numerator will be 108 - 4 = 106 milligrams. The denominator will be 6 - 2 = 4 minutes.

The fraction 106mg/4min simplifies to 26mg/min, or 26 milligrams per minute. Since the answer is positive, this tells us that every minute, the body gains an average of 26 more milligrams of medicine.

Hope this helps!

Answer 2

(108 - 4) / (6 - 2) = m (slope or rate of change)

Answer 3