Given the function  
f
(
x
)
=
960
(
0.75
)
x
  evaluate each of the following.

Note: Round your answers to two decimal places as needed.
A) Evaluate  
f
(
−
10
)
 	 
f
(
−
10
)
=
  

B) Evaluate  
f
(
−
5
)
 	 
f
(
−
5
)
=
  

C) Evaluate  
f
(
0
)
 	 
f
(
0
)
=
  

D) Evaluate  
f
(
5
)
 	 
f
(
5
)
=
  

E) Evaluate  
f
(
10
)
 	 
f
(
10
)
=

To evaluate the function \( f(x) = 960(0.75)^x \), we will substitute the given values of \( x \) and compute each expression.

### A) Evaluate \( f(-10) \)
\[
f(-10) = 960(0.75)^{-10} = 960 \cdot \frac{1}{(0.75)^{10}} \approx 960 \cdot 18.79 \approx 18043.84
\]
**Rounded:** \( f(-10) \approx 18043.84 \)

### B) Evaluate \( f(-5) \)
\[
f(-5) = 960(0.75)^{-5} = 960 \cdot \frac{1}{(0.75)^{5}} \approx 960 \cdot 4.57 \approx 4388.16
\]
**Rounded:** \( f(-5) \approx 4388.16 \)

### C) Evaluate \( f(0) \)
\[
f(0) = 960(0.75)^{0} = 960 \cdot 1 = 960
\]
**Rounded:** \( f(0) = 960.00 \)

### D) Evaluate \( f(5) \)
\[
f(5) = 960(0.75)^{5} \approx 960 \cdot 0.2373 \approx 228.02
\]
**Rounded:** \( f(5) \approx 228.02 \)

### E) Evaluate \( f(10) \)
\[
f(10) = 960(0.75)^{10} \approx 960 \cdot 0.0563 \approx 54.05
\]
**Rounded:** \( f(10) \approx 54.05 \)

### Summary of Results:
- A) \( f(-10) \approx 18043.84 \)
- B) \( f(-5) \approx 4388.16 \)
- C) \( f(0) = 960.00 \)
- D) \( f(5) \approx 228.02 \)
- E) \( f(10) \approx 54.05 \)

Would you like more details or have any questions? Here are some related questions you might consider:
1. How does the function behave as \( x \) increases?
2. What is the significance of the base \( 0.75 \) in this function?
3. Can we find the intercepts of the function graph?
4. How would the function change if the base were \( 0.5 \) instead?
5. What would be the long-term behavior of \( f(x) \) as \( x \) approaches infinity?

**Tip:** When evaluating exponential functions, remember that a negative exponent indicates a reciprocal, which can significantly affect the result.

Given the function f(x) = 960(0.75)^x evaluate f(-10), f(-5), f(0), f(5), f(10).

Explore the evaluation of the exponential function f(x) = 960(0.75)^x at various points. This solution provides detailed calculations for f(-10), f(-5), f(0), f(5), and f(10), rounding results to two decimal places.

Math Problem Statement

Given the function
f ( x )

f ( − 10 )

f ( − 5 )

f ( 0 )

f ( 5 )

f ( 10 )

Solution

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