Let's evaluate the function [tex]\( f(x) = 34 \cdot (0.86)^x \)[/tex] at the given points and round each result to the nearest hundredth.
1. Evaluate [tex]\( f(-3) \)[/tex]:
[tex]\[
f(-3) = 34 \cdot (0.86)^{-3}
\][/tex]
Continuing with the calculations and rounding to the nearest hundredth, we find:
[tex]\[
f(-3) = 53.45
\][/tex]
2. Evaluate [tex]\( f(-2) \)[/tex]:
[tex]\[
f(-2) = 34 \cdot (0.86)^{-2}
\][/tex]
After performing the necessary calculations and rounding to the nearest hundredth, we get:
[tex]\[
f(-2) = 45.97
\][/tex]
3. Evaluate [tex]\( f(-1) \)[/tex]:
[tex]\[
f(-1) = 34 \cdot (0.86)^{-1}
\][/tex]
Doing the calculations and rounding the result to the nearest hundredth, we obtain:
[tex]\[
f(-1) = 39.53
\][/tex]
4. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 34 \cdot (0.86)^0
\][/tex]
Since any number to the power of 0 is 1, we get:
[tex]\[
f(0) = 34.00
\][/tex]
5. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 34 \cdot (0.86)^1
\][/tex]
By completing the calculations and rounding to the nearest hundredth, we find:
[tex]\[
f(1) = 29.24
\][/tex]
6. Evaluate [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 34 \cdot (0.86)^2
\][/tex]
After calculating and rounding the result to the nearest hundredth, we get:
[tex]\[
f(2) = 25.15
\][/tex]
7. Evaluate [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = 34 \cdot (0.86)^3
\][/tex]
Completing the calculations and rounding the result to the nearest hundredth, we obtain:
[tex]\[
f(3) = 21.63
\][/tex]
Thus, the evaluated values of the function [tex]\( f(x) = 34 \cdot (0.86)^x \)[/tex] are:
[tex]\[
\begin{aligned}
f(-3) & = 53.45 \\
f(-2) & = 45.97 \\
f(-1) & = 39.53 \\
f(0) & = 34.00 \\
f(1) & = 29.24 \\
f(2) & = 25.15 \\
f(3) & = 21.63
\end{aligned}
\][/tex]
