Chapter 1.4, Problem 65E

(a)

To determine

To explain: Describe the transformation of graph.

Answer to Problem 65E

The graph of $N(t)=1.5{(t-4.8)}^2+123$ is shifted upward by 123 units and 4.8 units left.

Explanation of Solution

Given data:

A model of data:

  $N(t)=1.5{(t-4.8)}^2+123$

Calculation:

The graph of $F(t)=t^2$ and graph of $N(t)=1.5{(t-4.8)}^2+123$

  

The graph of $N(t)=1.5{(t-4.8)}^2+123$ is shifted upward by 123 units and 4.8 units left.

Conclusion:

The graph of $N(t)=1.5{(t-4.8)}^2+123$ is shifted upward by 123 units and 4.8 units left.

(b)

To determine

To graph: $N(t)=1.5{(t-4.8)}^2+123$

Explanation of Solution

Given data:

A model of data:

  $N(t)=1.5{(t-4.8)}^2+123$

Calculation:

  

Conclusion:

It is an increasing graph.

(c)

To determine

To represent: Equation at t=0 .

Answer to Problem 65E

The equation for representing t = 0 as 2010 is $N(t)=1.5{(t-14.8)}^2+123$

Explanation of Solution

Given data:

A model of data :

  $N(t)=1.5{(t-4.8)}^2+123$

Calculation:

The equation for representing t=0 as 2010 is:

As t is shifted 10 units backward

$\begin{array}{l}N(t)=1.5{(}^t+123\\ N(t)=1.5{(}^t+123\\ N(t)=1.5{(}^t+123\end{array}$

Conclusion:

The equation for representing t=0 as 2010 is $N(t)=1.5{(t-14.8)}^2+123$