Questions: Determine whether the equation represents exponential growth, exponential decay, or neither. y=300(1.05)^x growth decay neither

Solution Steps

To determine whether the equation represents exponential growth, exponential decay, or neither, we need to examine the base of the exponential function. 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 equal to 1, it is neither growth nor decay.

The given equation is \( y = 300(1.05)^x \). This is an exponential function of the form \( y = a \cdot b^x \), where \( a = 300 \) and \( b = 1.05 \).

The base of the exponential function is \( b = 1.05 \).

• If \( b > 1 \), the function represents exponential growth.
• If \( 0 < b < 1 \), the function represents exponential decay.
• If \( b = 1 \), the function is neither growth nor decay.

Since \( b = 1.05 \) and \( 1.05 > 1 \), the function represents exponential growth.

Final Answer