Question

Describe the end behavior and the percent rate of change of the exponential function shown on the graph.



As x
, y
, as x decreases, y approaches
.

The percent rate of change of this function is
%.

Answer 1

To analyze the end behavior and the percent rate of change of the given exponential function based on your description, we can outline the concepts. However, please note that specific details like the function's equation or the graph are required for precise calculations.

1. **End Behavior:**
- For an exponential function of the form \(y = a \cdot b^x\), where \(b > 1\):
- As \(x\) approaches infinity (\(x \to \infty\)), \(y\) approaches infinity (\(y \to \infty\)).
- As \(x\) approaches negative infinity (\(x \to -\infty\)), \(y\) approaches zero (\(y \to 0\).
- If \(0 < b < 1\):
- As \(x\) approaches infinity (\(x \to \infty\)), \(y\) approaches zero (\(y \to 0\)).
- As \(x\) approaches negative infinity (\(x \to -\infty\)), \(y\) approaches infinity (\(y \to \infty\).

Based on your description, you might be saying:
- As \(x\) **decreases**, \(y\) **approaches** 0 (which suggests an exponential decay, \(0 < b < 1\)).

2. **Percent Rate of Change:**
- The percent rate of change of an exponential function can be calculated using the formula:
\[
\text{Percent Rate of Change} = (b - 1) \times 100\%
\]
where \(b\) is the base of the exponential function.
- If the exponential growth factor (\(b > 1\)), the function represents growth, and if \(0 < b < 1\), it represents decay.

If you provide the specific function or characteristics from the graph, I can offer more accurate numerical values or a more complete description. For now, you can fill in the percent rate of change based on the calculated base \(b\).