To determine whether the function \( P(t) = 8.5(0.92)^{2} \) represents exponential growth or decay, we need to look at the base of the exponential part, which is \( 0.92 \).
If the base of the exponent is less than 1 (like 0.92), the function represents exponential decay. If the base were greater than 1, it would represent exponential growth.
In this case, since \( 0.92 < 1 \), we identify that \( P(t) \) represents exponential decay.
Next, to find the rate of change, we can calculate the decay rate from the base. The decay rate can be found using the formula \( r = 1 - b \), where \( b \) is the base of the exponential function.
Here, \( b = 0.92 \):
\[ r = 1 - 0.92 = 0.08 \]
To express this as a percentage, we convert it to:
\[ 0.08 \times 100% = 8% \]
Thus, we conclude:
- The function represents Exponential Decay.
- The rate of change is 8%.
The correct response is Exponential Decay; 8%.