   Chapter 11.6, Problem 59E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Grades62 A productivity formula for a student’s performance on difficult English examination is g = 4 t x − 0.2 t 2 − 10 x 2     ( t < 30 ) , where g is the score the student can expect to obtain, t is the number of hours of study for the examination, and x is the student’s grade-point average.a. For how long should a student with a 3.0 grade-point average study to score 80 on the examination?b. Find d t d x fora student who earns a score of 80, evaluate it when x = 3.0 , andinterpret the result.

(a)

To determine

To calculate: The study hours taken by a student with a 3.0 grade-point average to score 80 in the examination when the productivity formula for a student’s performance in English examination is given by the function g=4tx0.2t210x2 (t<30).

Explanation

Given information:

The function, g=4tx0.2t210x2 represents the productivity formula for a student’s performance in English examination where g is the expected score obtained by the student, t is the number of hours of study in the examination and x is the student’s grade-point average.

Formula used:

The value of x for the equation ax2+bx+c=0 by using the quadratic formula is,

x=b±b24ac2x.

Calculation:

Consider the function,

g=4tx0.2t210x2

Substitute g=80 and x=3 in the above function,

80=4t(3)0.2t210(3)2

Solve the above expression to evaluate the number of hours as,

80=4t(3)0.2t210(3)280=12t0

(b)

To determine

To calculate: The value of dtdx at x=3.0 for a student who scores 80 in the examination when the productivity formula for a student’s performance in English examination is given by the function g=4tx0.2t210x2 (t<30).

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