   Chapter 11.2, Problem 58E ### 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

# Blood pressure Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation p = 95 e − 0.491 t (a) Use the derivative to find the rate at which the pressure is changing at any time t.(b) Use the derivative to find the rate at which the pressure is changing after 0.1 second.(c) Is the pressure increasing or decreasing?

(a)

To determine

To calculate: The rate of change of pressure with respect to time t if the pressure of a normal adult is a function of time in second and can be modeled by the equation P=95e0.491t.

Explanation

Given Information:

The provided function is P=95e0.491t where t is time.

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,

P=95e0.491t

Where t is time.

Differentiate both sides with respect to t,

P(t)=ddt(95e0.491t)=95ddt(e0

(b)

To determine

To calculate: Rate of change of pressure for t=0.1 seconds.

(c)

To determine

Whether the pressure is increasing or decreasing.

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