Chapter 8.4, Problem 115E

i.

To determine

To calculate: $g(t)$ by shifting $f(t)$ by 30 units to the left.

Answer to Problem 115E

  $g(t)=0.0055t^2+0.303t+7.6$ .

Explanation of Solution

Given information: $f(t)=0.0055t^2-0.027t+3.46$ and $g(t)=f(t+30)$ .

Calculation:

Given function f, $f(t)=0.0055t^2-0.027t+3.46$

  $g(t)=f(t+30)$

  $\begin{array}{l}$ g(t)=0.0055{(t+30)}^2-0.027(t+30)+3.46$$ g(t)=0.0055(t^2+2\times 30t+{30}^2)-0.027(t+30)+3.46$g(t)=0.0055t^2+0.33t+4.95-0.027t-0.81+3.46\\ g(t)=0.0055t^2+0.303t+7.6\end{array}$

That is,

  $g(t)=0.0055t^2+0.303t+7.6$ .

ii.

To determine

To graph: The functions $g(t)$ and $f(t)$ .

Answer to Problem 115E

  

Explanation of Solution

Given information: $f(t)=0.0055t^2-0.027t+3.46$ and $g(t)=0.0055t^2+0.303t+7.6$ .

Calculation: