Questions: Evaluate the following function at the indicated values. Round to the nearest ten-thousandth. f(x) = e^(-2x) + 5 (a) f(-3) = (b) f(2) = (c) f(-1) =

Transcript text: Evaluate the following function at the indicated values. Round to the nearest ten-thousandth. \[ f(x)=e^{-2 x}+5 \] (a) $f(-3)=$ $\square$ (b) $f(2)=$ $\square$ (c) $\quad f(-1)=$ $\square$

Solution

Solution Steps

To evaluate the function $ f(x) = e^{-2x} + 5 $ at the given values, substitute each value of $ x $ into the function and compute the result. Use Python's math library to handle the exponential calculations and round the results to the nearest ten-thousandth.

Step 1: Evaluate $ f(-3) $

To find $ f(-3) $, we substitute $ x = -3 $ into the function: \[ f(-3) = e^{-2(-3)} + 5 = e^{6} + 5 \approx 408.4288 \]

Step 2: Evaluate $ f(2) $

Next, we evaluate $ f(2) $ by substituting $ x = 2 $: \[ f(2) = e^{-2(2)} + 5 = e^{-4} + 5 \approx 5.0183 \]

Step 3: Evaluate $ f(-1) $

Finally, we calculate $ f(-1) $ by substituting $ x = -1 $: \[ f(-1) = e^{-2(-1)} + 5 = e^{2} + 5 \approx 12.3891 \]