Question

Worker Efficiency An efficiency study showed that the average worker at Delphi Electronics assembled cordless telephones at the rate of $$ f(t)=-\frac{3}{2} t^{2}+6 t+10 \quad(0 \leq t \leq 4) $$ phones/hr, $t$ hr after starting work during the morning shift. At what rate does the average worker assemble telephones 2 hr after starting work?

Name: Problem 26, Chapter 2: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-19T06:21:16-08:00
Duration: 1 min 42 s
Channel: Priyanka Sadarangani
Description: Worker Efficiency An efficiency study showed that the average worker at Delphi Electronics assembled cordless telephones at the rate of f(t)=-(3)/(2) t^2+6 t+10 (0 ≤t ≤4) phones/hr, t hr after starting work during the morning shift. At what rate does the average worker assemble telephones 2 hr after starting work?

   Worker Efficiency An efficiency study showed that the average worker at Delphi Electronics assembled cordless telephones at the rate of
$$ f(t)=-\frac{3}{2} t^{2}+6 t+10 \quad(0 \leq t \leq 4) $$
phones/hr, $t$ hr after starting work during the morning shift. At what rate does the average worker assemble telephones 2 hr after starting work?

Applied Calculus for the Managerial, Life, and Social Sciences

Soo T. Tan 10th Edition

Chapter 2, Problem 26

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Solved by Expert Priyanka Sadarangani

05/19/2021

Step 1

Step 1: The rate at which the average worker assembles telephones is given by the function $$ f(t)=-\frac{3}{2} t^{2}+6 t+10 \quad(0 \leq t \leq 4) $$ where $t$ is the number of hours after starting work. Show more…

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Worker Efficiency An efficiency study showed that the average worker at Delphi Electronics assembled cordless telephones at the rate of $$ f(t)=-\frac{3}{2} t^{2}+6 t+10 \quad(0 \leq t \leq 4) $$ phones/hr, $t$ hr after starting work during the morning shift. At what rate does the average worker assemble telephones 2 hr after starting work?

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Key Concepts

Quadratic Functions

Quadratic functions are polynomial functions of degree 2, commonly expressed in the form ax² + bx + c. They are frequently used in modeling scenarios where the rate or other quantities change in a parabolic pattern, allowing for the analysis of maximum, minimum, or trend behaviors in various contexts.

Rate Functions

A rate function represents how one quantity changes with respect to another, typically time. In many applications, including productivity and efficiency studies, this type of function gives the instantaneous rate, indicating, for example, how many units are produced per hour at a specific time.

Function Evaluation

This concept involves substituting a specific value into a function to determine the corresponding output. It is a fundamental step when using mathematical models to predict or analyze behavior at a particular moment, such as evaluating a production rate at a given time.

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