   Chapter 10.4, Problem 14E ### 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

# Candidate recognition Suppose that in an election year, the proportion p of voters who recognize a certain candidate's name t months after the campaign started is given by p ( t ) = 7.2 t 2 + 36 + 0.2 After how many months is the proportion maximized?

To determine

To calculate: The number of months after which the proportion of voters in an election be maximized.

Explanation

Given Information:

The function is p(t)=7.2tt2+36+0.2

Where t denotes the number of months and p is the proportion of voters.

Formula used:

To find the maximum value, calculate the relevant stationary value of an equation. Differentiate the function with respect to the independent variable and equate it to 0. the relevant value is the stationary value that satisfies the provided conditions.

Quotient rule gives the derivative of a function when one differentiable function is divided by the other. To find the derivative of a function f(x)g(x), use

ddx[f(x)g(x)]=g(x)f'(x)f(x)g'(x)(g(x))2

Calculation:

Consider the provided statement,

The function is p(t)=7.2tt2+36+0.2

To find the stationary value for p(t)=7.2tt2+36+0.2, differentiate the equation with respect to the independent variable t to get

P'=7

### 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 33-38, rewrite the expression using positive exponents only. 33. (xy)2

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

#### Change 36 in. /s to mi/h

Elementary Technical Mathematics

#### True or False:

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