Chapter 8.2, Problem 70E

To determine

To show: whether the function is exponential growth or exponential decay. Also, sketch the graph of the function.

Answer to Problem 70E

The function represents exponential growth.

  

Explanation of Solution

Given information:

  $y=2e^x$

Formula used:

An exponential function has the form $y=a{b}^x$ , where $a\ne 0$ and the base b is a positive real number other than 1.

If $a>0$ and $b>1$ , then $y=a{b}^x$ is an exponential; decay function, and b is called the decay factor.

If $a>0$ and $0<b<1$ , then $y=a{b}^x$ is an exponential; decay function, and b is called the decay factor.

Calculation:

  $y=2e^x$

Step1. Identifying the value of the base.

Since, the base is $e=2.718281828$ , is greater than 1.

So, the function represents exponential growth.

Step2. Making of table with different values

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y$	$\begin{array}{l}y=2e^{(-2)}\\ =2(0.135335)\\ =0.27067\end{array}$	$\begin{array}{l}y=2e^{(-1)}\\ =2(\mathrm{0.0.367879})\\ =0.735758\end{array}$	$\begin{array}{l}y=2e^{(0)}\\ =2(1)\\ =2\end{array}$	$\begin{array}{l}y=2e^{(1)}\\ =2(2.718281)\\ =5.436562\end{array}$	$\begin{array}{l}y=2e^{(2)}\\ =2(7.389056)\\ =14.778112\end{array}$	$\begin{array}{l}y=2e^{(3)}\\ =2(20.085536)\\ =40.171072\end{array}$

Step3. Plotting the points.

  

Figure1.

Step4. Start drawing the graph from left to right. A smooth curve that begins just above the x -axis, passes through the plotted points, moves up to the right.