Explanation Given: Rate at which revenue was generated over the time is: f ( t ) = 10 e .1 t ( 7 ≤ t ≤ 17 ) and rate at which cost was incurred is approximated by: g ( t ) = 3 + 2 t ( 7 ≤ t ≤ 17 ) Year 2007 corresponds to t = 7 . Formula used: Area between two curves: If two functions f and g is continuous function and the also f ( x ) ≥ g ( x ) on the interval [ a , b ] then the area between the graph between the interval [ a , b ] is given by following expression: ∫ a b [ f ( x ) − g ( x ) ] d x Definite integral property: ∫ a b f ( x ) d x = F ( b ) − F ( a ) Here, F ( x ) is the antiderivative of f ( x ) . Calculation: The profit will be the area formed between revenue curve to the cost curve in the given time span. The area under the curves are obtained from following expression. Total profit = ∫ 7 17 [ f ( t ) − g ( t ) ] = ∫ 7 17 ( 10 e 0

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

See similar textbooks

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

Videos

Question

Chapter 13.6, Problem 3CP

To determine

To calculate: The total profit over the 10-year period start from year 2007 to end of 2016, if the rate at which revenue was generated over the time is f(t)=10e.1t and rate at which cost was incurred is approximated by g(t)=3+2t.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.6, Problem 2CP

Chapter 13.6, Problem 4CP

Students have asked these similar questions

Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?

The price P of gasoline increases to a maximum and then stays at a fixed price. What is the rate of change dp/dt and how is it changing at the time when the price reaches a maximum?a. dp/dt is negative at the maximum and is decreasing.b. dp/dt is equal to zero at the maximum and remains the same.c. dp/dt is positive at the maximum and is decreasing.d. dp/dt is negative at the maximum and is increasing.

Macros Chemical Company is trying produce a test batch of a new organic fertilizer made from a proprietary type of green algae. The fertilizer is an experimental mixture of 4 ingedients: salt, water, soil, and algae (all measured in liters). In order to remain stable, the ratio of salt to water must be 5 to 8. In addition, the number of liters of salt and soil combined must always be the same as the number of liters of algae and water combined. How many liters of each compound should be included to create 110 liters of the fertilizer? Set up a system of equations, and then solve using your calculator. Use the variables in order in your equations as x, y, z, w as shown below in part a. MAKE SURE IT IS MATRIX FORM!a) Solve the system; write the solutions here, using tt as the parameter as needed. Solution:x= liters of salt ;y= liters of water ;z= liters of soil ; andw= liters of algae.b) If 14.9 liters of algae are to be used for a batch, how much of each compund will be…

Chapter 13 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The total profit over the 10-year period start from year 2007 to end of 2016 , if the rate at which revenue was generated over the time is f ( t ) = 10 e .1 t and rate at which cost was incurred is approximated by g ( t ) = 3 + 2 t .

Solution Summary: The author calculates the total profit over the 10-year period starting from year 2007 to end of 2016.

Concept explainers

Videos

To calculate: The total profit over the 10-year period start from year 2007 to end of 2016, if the rate at which revenue was generated over the time is f(t)=10e.1t and rate at which cost was incurred is approximated by g(t)=3+2t.

Want to see the full answer?

Chapter 13 Solutions