Question

After surgery you are given a pain reliever, the level of the medication will decrease slowly

over time. Let C(t) represent the medicine's concentration in your body. Write an expression
for the rate of change of the medicine's concentration level over the period from t = 15
minutes to t = 90 minutes.

Answer 1

Answer: C(90) - C(15)/90 - 15

Explanation:

The function for finding average rate of change is f(x)2 - f(x)1/x2 - x1.

The y = C(t), the x = t.

You are given two x intervals, 90 and 15.

90 is x2, 15 is x1.

You plug in your x points into the function.

C(90) - C(15)/90 - 15.

Answer 2

Explanation:

To find the expression for the rate of change of the medicine's concentration level from t = 15 minutes to t = 90 minutes, you can use the concept of a derivative in calculus. The rate of change of concentration with respect to time is represented by the derivative C'(t) of the concentration function C(t).

So, you need to find C'(t) for the given time interval [15 minutes, 90 minutes]. You'll want to compute the difference in concentration at these two times and divide it by the difference in time:

C'(t) = [C(90 minutes) - C(15 minutes)] / [90 minutes - 15 minutes]

This expression gives you the average rate of change of the medicine's concentration over the time interval from t = 15 minutes to t = 90 minutes. If you have a specific function C(t) that describes the concentration over time, you can plug in the values for C(90 minutes) and C(15 minutes) into the expression to calculate the rate of change.

Keep in mind that to find the instantaneous rate of change at a specific time t within this interval, you would need to take the limit as the interval approaches zero, which would involve the derivative C'(t).