Evaluate the function at the given value of x. Round your result to three decimal places. Function: f(x)=$$ 0.4^{x} $$ Value: x=1.7 

To evaluate the function $ f(x) = 0.4^x $ at $ x = 1.7 $, we follow these steps:

### Step-by-step calculation:

1. **Apply the given value of $ x $**:
   \[
   f(1.7) = 0.4^{1.7}
   \]
   
2. **Use a calculator to find the value**:
   \[
   f(1.7) \approx 0.4^{1.7} \approx 0.1985
   \]

3. **Round to three decimal places**:
   \[
   f(1.7) \approx 0.199
   \]

Thus, the value of the function at $ x = 1.7 $ is approximately **0.199**.

Do you need further details on this process or have any questions?

### Related Questions:
1. What is $ f(x) = 0.4^x $ when $ x = 2.5 $?
2. How does changing the base (0.4) affect the behavior of the function as $ x $ increases?
3. What is the derivative of $ f(x) = 0.4^x $?
4. What would $ f(x) = 0.4^x $ look like graphically?
5. How do fractional exponents affect the value of exponential functions?

### Tip:
For exponential functions with a base less than 1 (like 0.4), the function decreases as $ x $ increases.

Evaluate the function at the given value of x. Round your result to three decimal places. Function: f(x)= 0.4^x Value: x=1.7

Discover how to evaluate the exponential function f(x) = 0.4^x at x = 1.7. Follow a step-by-step guide to calculate the value of the function, round the result to three decimal places, and understand key concepts like exponential decay and fractional exponents. Suitable for students in Grades 9-11.

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