Write the function for the data in this table.
x          y 
0         0.04
1          0.2
2          1
3          5
4         25


The data in the table appears to represent exponential growth. Let's analyze the \(x\) and \(y\) values to find the relationship:

| \(x\) | \(y\)  |
|------|--------|
|  0   |  0.04  |
|  1   |  0.2   |
|  2   |  1     |
|  3   |  5     |
|  4   |  25    |

By observing the pattern, each \(y\)-value seems to be multiplied by 5 as \(x\) increases by 1. This suggests the relationship:

\[
y = 0.04 \times 5^x
\]

So, the function can be written as:

\[
y = 0.04 \times 5^x
\]

### Explanation:
- When \(x = 0\), \(y = 0.04\), which matches the given value.
- When \(x = 1\), \(y = 0.04 \times 5 = 0.2\).
- When \(x = 2\), \(y = 0.04 \times 5^2 = 1\).
- When \(x = 3\), \(y = 0.04 \times 5^3 = 5\).
- When \(x = 4\), \(y = 0.04 \times 5^4 = 25\).

### Would you like further details or have any questions?

Here are 5 relative questions based on the function:

1. How does the function behave as \(x\) becomes very large?
2. What is the significance of the base 5 in the function?
3. Can you rewrite the function in logarithmic form?
4. How would you find the inverse of this function?
5. How would a change in the coefficient 0.04 affect the function?

**Tip:** The base in exponential functions determines the rate of growth or decay, with larger bases resulting in faster growth.

Write the function for the data in this table.
x          y 
0         0.04
1          0.2
2          1
3          5
4         25

Discover the exponential function y = 0.04 × 5^x derived from the data points (0, 0.04), (1, 0.2), (2, 1), (3, 5), and (4, 25). This problem introduces exponential growth concepts and algebraic function analysis, ideal for Grades 9-12.

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