Chapter 2.1, Problem 30E

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

Finite Mathematics and Applied Cal...

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

GE Net Income 2007–2011 The annual net income of General Electric for the period 2007–2011 could be approximated by P ( t ) = 1.6 t 2 − 15 t + 46 billion dollars ( 2 ≤ t ≤ 6 ) , where t is time in years since the start of 2005.6 According to the model, during what year in this period was General Electric’s net income lowest? What was the corresponding net income? Would you trust this model to continue to be valid long past this period? Why or why not?

To determine

To calculate: The year for which general Electric net income is lowest, corresponding net income for the following annual income equation for the period 20072011,

P(t)=1.6t215t+46

billion dollars for 2t6

Where time t is in years. Also justify that would you trust this model to be continue for a longer period.

Explanation

Given Information:

The provided annual income equation is:

P(t)=1.6t2ā15t+46

Formula Used:

The vertex formula for a quadratic function f(x)=ax2+bx+c

is given by:

x=āb2a

Calculation:

Consider the given annual income equation,

P(t)=1.6t2ā15t+46

Compare the equation P(t)=1.6t2ā15t+46 with the standard function f(x)=ax2+bx+c and find the value of a,b and c.

The values are a=1.6,b=ā15 and c=46.

Here a<0

, therefore the corresponding parabola will be downward facing and vertex will be the highest point.

To calculate the year for which net income will be highest calculate the coordinates of the vertex.

Vertex: The highest point for which the coordinates are maximum, formula of x- coordinate of vertex is,

t=āb2a

Substitute a=1

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