   Chapter 10.4, Problem 13E ### 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

# News impact Suppose that the percent p (as a decimal) of people who could correctly identify two of eight defendants in a drug case t days after their trial began is given by p ( t ) = 6.4 t t 2 + 64 + 0.05 Find the number of days before the percent is maximized and find the maximum percent.

To determine

To calculate: The number of days to maximize the percent of people and the maximum percent.

Explanation

Given Information:

The percent of people is given as

p(t)=6.4tt2+64+0.05

Where t denotes the number of days.

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.

If the second derivative of the provided function is less than zero, then substituting the value of the independent variable will give the maximum value of the equation.

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:

The percent of people is given as

p(t)=6.4tt2+64+0.05

Where t denotes the number of days.

To find the stationary value for p(t)=6.4tt2+64+0.05, differentiate the equation with respect to the independent variable t to get

P'=6.4(t2+64)6.4t×2t(t2+64)2=6.4(t22t2+64)(t2+64)=6.4(t2+64)(t2+64)2

Put P'=0 to get t,

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