Questions: Determine whether the following equation represents exponential growth, exponential decay, or neither. y=10(2.3)^(0.5 x) growth decay neither

Solution Steps

To determine whether the given equation represents exponential growth, exponential decay, or neither, we need to analyze the base of the exponent. If the base is greater than 1, it represents exponential growth. If the base is between 0 and 1, it represents exponential decay. If the base is negative or 1, it represents neither.

1. Extract the base of the exponent from the given equation.
2. Check if the base is greater than 1, between 0 and 1, or neither.

The given equation is

\[ y = 10(2.3)^{0.5x} \]

From this equation, we can identify the base of the exponent as \( 2.3 \).

Next, we analyze the base \( 2.3 \). Since \( 2.3 > 1 \), this indicates that the function is increasing as \( x \) increases.

Since the base is greater than 1, we conclude that the equation represents exponential growth.

Final Answer