Questions: Without graphing, describe the shape of the graph of the function. Find the second coordinates of the points with first coordinates 0 and 1. f(x)=e^(-1.6 x) The graph exponentially decays. Find the second coordinates of the given first coordinates x f(x)=e^(-1.6 x) 0 f(0)=1 1 f(1)= (Round to one decimal place as needed.)

Without graphing, describe the shape of the graph of the function. Find the second coordinates of the points with first coordinates 0 and 1.

f(x)=e^(-1.6 x)

The graph exponentially decays.
Find the second coordinates of the given first coordinates

x f(x)=e^(-1.6 x)
0 f(0)=1
1 f(1)=

(Round to one decimal place as needed.)

Transcript text: Without graphing, describe the shape of the graph of the function. Find the second coordinates of the points with first coordinates 0 and 1. \[ f(x)=e^{-1.6 x} \] The graph exponentially decays. Find the second coordinates of the given first coordinates \[ \begin{array}{ll} \mathbf{x} & f(x)=e^{-1.6 x} \\ 0 & f(0)=1 \\ 1 & f(1)=\square \end{array} \] (Round to one decimal place as needed.)

Solution

Solution Steps

To find the second coordinates of the points with first coordinates 0 and 1 for the function \( f(x) = e^{-1.6x} \), we need to evaluate the function at these points. For \( x = 0 \), the function simplifies to \( f(0) = e^0 = 1 \). For \( x = 1 \), we calculate \( f(1) = e^{-1.6} \) and round the result to one decimal place.

Step 1: Evaluate \( f(0) \)

To find the second coordinate when the first coordinate is \( 0 \), we evaluate the function: \[ f(0) = e^{-1.6 \cdot 0} = e^0 = 1 \]

Step 2: Evaluate \( f(1) \)

Next, we find the second coordinate when the first coordinate is \( 1 \): \[ f(1) = e^{-1.6 \cdot 1} = e^{-1.6} \approx 0.2012 \] Rounding this value to one decimal place gives us \( 0.2 \).