A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f (x) with entries 0.004, 0.02, 0.1, 0.5.
What is the growth factor of the exponential function represented by the table?

0.2
0.1
5
20

To determine the growth factor of the exponential function, we can observe the pattern in the function values \( f(x) \) as \( x \) increases.

The values in the table are:

\[
\begin{array}{c|c}
x & f(x) \\
\hline
-2 & 0.004 \\
-1 & 0.02 \\
0  & 0.1 \\
1  & 0.5 \\
\end{array}
\]

An exponential function is of the form:

\[
f(x) = a \cdot b^x
\]

where \( a \) is the initial value (when \( x = 0 \)) and \( b \) is the growth factor.

From the table, we see that when \( x = 0 \), \( f(0) = 0.1 \). Therefore, \( a = 0.1 \).

Now, we calculate the ratio of consecutive values to find the growth factor \( b \). Let's compute the ratio between successive values of \( f(x) \):

\[
\frac{f(-1)}{f(-2)} = \frac{0.02}{0.004} = 5
\]

\[
\frac{f(0)}{f(-1)} = \frac{0.1}{0.02} = 5
\]

\[
\frac{f(1)}{f(0)} = \frac{0.5}{0.1} = 5
\]

The ratio between each pair of consecutive function values is 5, meaning the growth factor \( b \) is 5.

Therefore, the growth factor is \( \boxed{5} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you derive the formula of an exponential function?
2. How do you find the initial value of an exponential function from a table?
3. What is the significance of the growth factor in an exponential function?
4. Can the growth factor of an exponential function be less than 1?
5. How can you determine if a function is exponential by looking at its table of values?

**Tip:** The growth factor in an exponential function determines how fast the function increases or decreases with each step in \(x\).

A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f (x) with entries 0.004, 0.02, 0.1, 0.5. What is the growth factor of the exponential function represented by the table? Options: 0.2, 0.1, 5, 20.

Discover how to find the growth factor of an exponential function using a table of values. In this problem, the growth factor is calculated from the function values for x = -2, -1, 0, and 1, leading to a result of 5. Perfect for students in Grades 9-12.

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