Question

1. use the graph of $y = e^x$ to evaluate the expression $e^{-2.8}$. round the solution to the nearest tenth if necessary

Explanation:

Step1: Identify the function

The graph is of \( y = e^x \), but we need to evaluate \( e^{-2.8} \). Note that \( e^{-x}=\frac{1}{e^x} \), so we can use the graph of \( y = e^x \) at \( x = 2.8 \) and take the reciprocal, or recognize that \( y = e^{-x} \) is the reflection of \( y = e^x \) over the y - axis.

Step2: Evaluate using the graph or calculator approximation

Using a calculator (since we can also calculate \( e^{-2.8}\) directly), we know that \( e^{-2.8}=\frac{1}{e^{2.8}}\). We know that \( e^{2.8}\approx16.4446\), so \( \frac{1}{16.4446}\approx0.0608\), which rounds to 0.1 when rounded to the nearest tenth. Also, from the graph of \( y = e^{-x} \) (the given graph seems to be of \( y = e^{-x} \) as it is a decreasing exponential curve), when \( x = 2.8 \), we can estimate the y - value. Looking at the options, 0.1 is the closest when rounded to the nearest tenth.

Answer:

0.1