   Chapter 5.5, Problem 81E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 100e−0.01t liters per minute. How much oil leaks out during the first hour?

To determine

To calculate: The oil leakage during the first hour.

Explanation

Given:

The function is r(t)=100e0.01t.

Calculation:

The integral function is,R(t)=060r(t)dt.

Substitute (100e0.01t) for r(t).

R(t)=060(100e0.01t)dt (1)

The region lies between t=0 and t=60.

Let u=0.01t (2)

Differentiate both sides of the Equation (2).

du=0.01dtdt=10.01du

Substitute 0 for t in Equation (2) and obtain the lower limit of u.

u=0.01(0)=0

Substitute 60 for t in Equation (2) and obtain the upper limit of u.

u=0.01(60)=0.6

Express the given integral in terms of u.

Substitute u for (0.01t) and (10

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 58, evaluate the expression. 7. |2 6|

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problem 31-38, write the equation of each line described. 38. Shown in the graph

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: If the three limits exist, then .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 