To determine the multiplicative rate of change of the function \( f(x) = 2 \cdot 5^x \), we need to identify how the function changes as \( x \) increases. Specifically, we need to find the factor by which the function value increases when \( x \) increases by 1 unit.
Given the function:
\[ f(x) = 2 \cdot 5^x \]
First, let's calculate the values of \( f(x) \) at different points:
- When \( x = 1 \):
\[ f(1) = 2 \cdot 5^1 = 2 \cdot 5 = 10 \]
- When \( x = 2 \):
\[ f(2) = 2 \cdot 5^2 = 2 \cdot 25 = 50 \]
- When \( x = 3 \):
\[ f(3) = 2 \cdot 5^3 = 2 \cdot 125 = 250 \]
Next, we must identify how \( f(x) \) changes as \( x \) increases by 1 unit. We can do this by examining the ratio of successive terms:
\[
\frac{f(2)}{f(1)} = \frac{50}{10} = 5
\]
\[
\frac{f(3)}{f(2)} = \frac{250}{50} = 5
\]
In both cases, the ratio is \( 5 \). This consistent ratio indicates that the function \( f(x) \) is multiplied by \( 5 \) each time \( x \) increases by 1 unit. Thus, the multiplicative rate of change of the function \( f(x) = 2 \cdot 5^x \) is:
\[
\boxed{5}
\]
The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function?
2
5
10
32
1 answer