Chapter 3.1, Problem 51E

To determine

Draw the graph and also construct a value table of the given function $s(t)=2e^{-0.12t}$ by using graphing utility, and also find any asymptotes of the graph.

Explanation of Solution

Given information:

It is given in the question that the given exponential function is $s(t)=2e^{-0.12t}$ .

Graph:

Interpretation:

By putting the values of t in the given function we get the value of y and then plot it and make the graph of the given function $s(t)=2e^{-0.12t}$ .

By putting $t=-2$ ,

  $\begin{array}{l}s(t)=2e^{-0.12t}\\ =2e^{-0.12(-2)}\\ =2e^{0.24}\\ =2*1.271\\ =2.542\end{array}$

By putting $t=-1$ ,

  $\begin{array}{l}s(t)=2e^{-0.12t}\\ =2e^{-0.12(-1)}\\ =2e^{0.12}\\ =2*1.127\\ =2.254\end{array}$

By putting $t=0$ ,

  $\begin{array}{l}s(t)=2e^{-0.12t}\\ =2e^{-0.12(0)}\\ =2e^0\\ =2*1\\ =2\end{array}$

By putting $t=1$ ,

  $\begin{array}{l}s(t)=2e^{-0.12t}\\ =2e^{-0.12(1)}\\ =2e^{-0.12}\\ =2*0.886\\ =1.773\end{array}$

By putting $t=2$ ,

  $\begin{array}{l}s(t)=2e^{-0.12t}\\ =2e^{-0.12(2)}\\ =2e^{-0.24}\\ =2*0786\\ =1.573\end{array}$

So the table is,

$t$	$s(t)=2e^{-0.12t}$
-2	2.542
-1	2.254
0	2
1	1.773
2	1.573

And asymptotes is

  $y=0$ .