   Chapter 11.2, Problem 49E ### 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

# Drugs in a bloodstream The percent concentration y of a certain drug in the bloodstream at any time t (in hours) is given by y = 100 ( 1 − e − 0.462 t ) (a) What function gives the instantaneous rate of change of the concentration of the drug in the bloodstream?(b) Find the rate of change of the concentration after 1 hour. Give your answer to three decimal places.

(a)

To determine

To calculate: The function which gives the instantaneous rate of change of concentration of the drug in the bloodstream if the percentage concentration y of a certain drug in the bloodstream at any time t is y=100(1e0.462t).

Explanation

Given Information:

The provided function is,

y=100(1e0.462t)

Where, t is the number of hours.

Formula used:

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

Calculation:

Consider the provided function,

y=100(1e0.462t)

Where, t is the number of hours.

Differentiate both sides with respect to t,

dydt=ddt(100(1e0.462t))=100ddt(1e0.462t)

A derivative of a constant number is zero,

dydt=100ddt(1e0

(b)

To determine

To calculate: Rate of change of concentration after 1 an hour if the function which gives the instantaneous rate of change of concentration of a drug in the bloodstream is 46.2e0.462t.

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