Question

Evaluating Exponential Functions Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals.

$h\left(x\right)=e^x;h\left(1\right),h\left(\pi \right),h(-3),h\left(\sqrt{2}\right)$

Short answer

Required values are $h\left(1\right)=2.718,h\left(\pi \right)=23.141,h(-3)=0.050,h\left(\sqrt{2}\right)=4.113$.

Step-by-step solution

Step 1. Given.

The given function is $h\left(x\right)=e^x$.

Step 2. To determine.

We have to find the values $h\left(1\right),h\left(\pi \right),h(-3),h\left(\sqrt{2}\right)$.

Step 3. Calculation.

In order to find$h\left(1\right),h\left(\pi \right),h(-3),h\left(\sqrt{2}\right)$ we will plug$x=1,\pi ,-3,\sqrt{2}$ respectively in the given function. We will use calculator to find these values.

$$\begin{gathered} h\left(1\right)=e^1 \\ =2.718 \end{gathered}$$

$$\begin{gathered} h\left(\pi \right)=e^{\pi } \\ =23.141 \end{gathered}$$

$$\begin{gathered} h\left(-3\right)=e^{-3} \\ =0.049787 \\ \approx 0.050 \end{gathered}$$

$$\begin{gathered} h\left(\sqrt{2}\right)=e^{\sqrt{2}} \\ =4.113 \end{gathered}$$

Hence,$h\left(1\right)=2.718,h\left(\pi \right)=23.141,h(-3)=0.050,h\left(\sqrt{2}\right)=4.113$