Question

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

$h\left(x\right)=e^{-3x};h\left(\frac{1}{3}\right),h\left(1.5\right),h(-1),h\left(-\pi \right)$

Short answer

Required values are $h\left(\frac{1}{3}\right)=0.368,h\left(1.5\right)=0.011,h(-1)=20.086,h\left(-\pi \right)=12391.648$.

Step-by-step solution

Step 1. Given.

The given function is $h\left(x\right)=e^{-3x}$.

Step 2. To determine.

We have to find the values $h\left(\frac{1}{3}\right),h\left(1.5\right),h(-1),h\left(-\pi \right)$.

Step 3. Calculation.

In order to find$h\left(\frac{1}{3}\right),h\left(1.5\right),h(-1),h\left(-\pi \right)$ we will plug$x=\frac{1}{3},1.5,-1,-\pi$ respectively in the given function. We will use calculator to find these values.

$$\begin{gathered} h\left(\frac{1}{3}\right)=e^{-3\left(\frac{1}{3}\right)} \\ =e^{-1} \\ =0.367879441171 \\ \approx 0.368 \end{gathered}$$

$$\begin{gathered} h\left(1.5\right)=e^{-3\left(1.5\right)} \\ =0.0111089965382 \\ \approx 0.011 \end{gathered}$$

$$\begin{gathered} h\left(-1\right)=e^{-3\left(-1\right)} \\ =e^3 \\ =20.0855369232 \\ \approx 20.086 \end{gathered}$$

width="97" height="48" role="math">h2=e2=4.113

Hence, $h\left(\frac{1}{3}\right)=0.368,h\left(1.5\right)=0.011,h(-1)=20.086,h\left(-\pi \right)=12391.648$.