Questions: Determine whether the equation represents exponential growth, exponential decay, or neither. y=200(0.98)^t 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 or less than 0, it represents neither.

The given equation is \( y = 200(0.98)^{t} \). Here, the base of the exponential function is \( 0.98 \).

To determine the nature of the exponential function, we analyze the base:

• If \( b > 1 \), it represents exponential growth.
• If \( 0 < b < 1 \), it represents exponential decay.
• If \( b = 1 \) or \( b \leq 0 \), it represents neither.

Since \( 0 < 0.98 < 1 \), we conclude that the function represents exponential decay.

Final Answer