   Chapter 11.2, Problem 52E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Drug concentration Suppose the concentration C ( t ) , in mg/ml, of a drug in the bloodstream t minutes after an injection is given by C ( t ) = 20 t e − 0.04 t (a) Find the instantaneous rate of change of the concentration after 10 minutes.(b) Find the maximum concentration and when it occurs.

(a)

To determine

To calculate: The instantaneous rate of change of the concentration of drug in the bloodstream after 10 minutes when the concentration of a drug is represented by C(t)=20te0.04t.

Explanation

Given Information:

The concentration of a drug is represented by C(t) in t minutes after injection into the bloodstream. The concentration of drugs is represented by, C(t)=20te0.04t.

Formula used:

The derivative of the exponential function,

ddx(ex)=ex

The simple power rule of differentiation,

ddx(xn)=nxn1

The product rule of two differentiable functions is,

ddx[f(x)g(x)]=f(x)ddx[g(x)]+g(x)ddx[f(x)]

Calculation:

Consider the concentration function provided, C(t)=20te0.04t.

Use the product rule to differentiate the provided concentration function,

C(t)=ddt(20te0.04t)=20ddt(te0.04t)=20[(t)ddt(e0

(b)

To determine

To calculate: The maximum concentration of the drugs in the bloodstream and the time at which it occurs.

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