Questions: Function Evaluation Given the function (f(x)=23(0.71)^x), evaluate each of the following. Round answers to the nearest hundredth as needed. (f(-3)=) (f(-2)=) (f(-1)=) (f(0)=) (f(1)=) (f(2)=) (f(3)=)

Function Evaluation
Given the function (f(x)=23(0.71)^x), evaluate each of the following.
Round answers to the nearest hundredth as needed.

(f(-3)=)
(f(-2)=)
(f(-1)=)
(f(0)=)
(f(1)=)
(f(2)=)
(f(3)=)

Transcript text: Function Evaluation Given the function $f(x)=23(0.71)^{x}$, evaluate each of the following. Round answers to the nearest hundredth as needed. \[ \begin{array}{c} f(-3)= \\ f(-2)= \\ f(-1)= \\ f(0)= \\ f(1)= \\ f(2)= \\ f(3)= \end{array} \]

Solution

Solution Steps

Step 1: Evaluate $ f(-3) $

To evaluate the function at $ x = -3 $: \[ f(-3) = 23(0.71)^{-3} = 23 \cdot \frac{1}{(0.71)^3} \approx 64.26 \]

Step 2: Evaluate $ f(-2) $

To evaluate the function at $ x = -2 $: \[ f(-2) = 23(0.71)^{-2} = 23 \cdot \frac{1}{(0.71)^2} \approx 45.63 \]

Step 3: Evaluate $ f(-1) $

To evaluate the function at $ x = -1 $: \[ f(-1) = 23(0.71)^{-1} = 23 \cdot \frac{1}{0.71} \approx 32.39 \]

Final Answer

\[ \begin{align_} f(-3) & = 64.26 \\ f(-2) & = 45.63 \\ f(-1) & = 32.39 \\ \end{align_} \] Thus, the answers are: \[ \boxed{f(-3) = 64.26, \, f(-2) = 45.63, \, f(-1) = 32.39} \]

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