Question

Write the exponential function.
x
​f(x)
0
1010
1
5050
2
250250
3
12501250
4
62506250
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Part 1
The exponential function is ​f(x)equals=enter your response here.
​(Use integers or fractions for any numbers in the​ expression.)

Answer 1

Based on the values provided, we can see the pattern in the function:

- For \( x = 0, f(x) = 10 \)
- For \( x = 1, f(x) = 50 \)
- For \( x = 2, f(x) = 250 \)
- For \( x = 3, f(x) = 1250 \)
- For \( x = 4, f(x) = 6250 \)

Observing the values of \( f(x) \), it looks like they follow the pattern of multiplication by 5:

1. \( f(0) = 10 \)
2. \( f(1) = 10 \times 5 = 50 \)
3. \( f(2) = 10 \times 5^2 = 250 \)
4. \( f(3) = 10 \times 5^3 = 1250 \)
5. \( f(4) = 10 \times 5^4 = 6250 \)

From this pattern, we can generalize the function as:
\[
f(x) = 10 \cdot 5^x
\]

So, the exponential function is:
\[
f(x) = 10 \cdot 5^x
\]