Explanation Given Information: The cost of producing a bottle 12 weeks into the year is $ 1.50 . Formula Used: If f ( x ) and g ( x ) are two functions then sum and difference rules for an integral is, ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x The rule for integral of constant term ∫ a d x = a x + C . If the function is f ( x ) = sin x , then the formula for the integration of the function is, ∫ sin ( a x ) d x = − 1 a cos ( a x ) + C . Constant multiple rule is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. Calculation: Consider the provided function 0.04 − 0.1 sin [ π 26 ( t − 25 ) ] . To evaluate the integral ∫ 0.04 − 0.1 sin [ π 26 ( t − 25 ) ] d t , suppose that the function f ( u ) is 0.04 and g ( u ) is 0.1 sin [ π 26 ( t − 25 ) ] . Apply the difference rule, ∫ [ f ( u ) − g ( u ) ] d u = ∫ f ( u ) d u − ∫ g ( u ) d u ∫ 0.04 − 0.1 sin [ π 26 ( t − 25 ) ] d t = ∫ 0.04 d t − ∫ 0.1 sin [ π 26 ( t − 25 ) ] d t Now, evaluate the integral of the function ∫ 0.04 d t by applying formula for constant integration and evaluate the integral of ∫ 0.1 sin [ π 26 ( t − 25 ) ] d t by applying constant multiple rules and using shortcut formula of ∫ sin ( a x ) d x = − 1 a cos ( a x ) + C to determine the cost C ( t ) . ∫ 0.04 d t − ∫ 0.1 sin [ π 26 ( t − 25 ) ] d t = ∫ 0

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 16.3, Problem 59E

To determine

To calculate: The cost C(t) at time t of producing a bottle of suntan lotion which is changing at rate of 0.04−0.1sin[π26(t−25)] dollars per week, t weeks after January.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.3, Problem 58E

Chapter 16.3, Problem 60E

Students have asked these similar questions

An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ No

4.1 Basic Rules of Differentiation. 1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with appropriate derivative notation. a) y=8x-5x3 4 X b) y=-50 √x+11x -5 c) p(x)=-10x²+6x3³

Please refer below

Chapter 16 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

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

The cost C ( t ) at time t of producing a bottle of suntan lotion which is changing at rate of 0.04 − 0.1 sin [ π 26 ( t − 25 ) ] dollars per week, t weeks after January.

Solution Summary: The author calculates the cost of producing a bottle of suntan lotion which is changing at rate of 0.04-0.1mathrmsinleft, t weeks after January.

Concept explainers

Videos

To calculate: The cost C(t) at time t of producing a bottle of suntan lotion which is changing at rate of 0.04−0.1sin[π26(t−25)] dollars per week, t weeks after January.

Want to see the full answer?

Chapter 16 Solutions