Question

a. The quantity (in mg) of a drug in blood at time t(in minutes) is given by Q= 25(0.8t).Estimate the rate of change of the quantity by computing the average rate of change over the interval near t= 3 and interpreting your answer using complete sentences with units

b. Sketch the graph of a function of your choice that has three critical points, two inflection points, one x-intercept, and one y-intercept. Please label all of the above mentioned points in your graph.

Answer 1

a). We estimate the rate of change at t = 3 by computing the average rate of change over intervals near t = 3.

We can make our estimate as accurate as we like by choosing our intervals small enough.

Let's look at the average rate of change over the interval 3 t 3.01:

The average rate of change = Qt

=25(0.8)3.01 25(0.8)33.01 3.00

=12.7715 12.803.01 3.00

= 2.85.

A reasonable estimate for the rate of change of the quantity at t = 3 is 2.85.

Since Q is in mg and t in minutes, the units of Q/t are mg/minute.

Since the rate of change is negative, the quantity of the drug is decreasing.

After 3 minutes, the quantity of the drug in the body is decreasing at 2.85 mg/minute.

The answer to the b part is in the pic. If any doubt still remained, let me know in the comment section. If this solution helped, please upvote to encourage us. Thanks ☺

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