To determine whether the function \( P(t) = 8.5(0.92)^t \) represents exponential growth or decay, we can look at the base of the exponent, which is 0.92.
- If the base is greater than 1, the function represents exponential growth.
- If the base is between 0 and 1 (as it is here with 0.92), the function represents exponential decay.
Since 0.92 is less than 1, this function represents exponential decay.
Next, we need to find the percentage rate of change. The formula for the percentage rate of change in an exponential decay function is given by:
\[ \text{Rate of change} = (1 - \text{base}) \times 100 \]
In this case:
\[ \text{Rate of change} = (1 - 0.92) \times 100 = 0.08 \times 100 = 8% \]
So, the function represents exponential decay with a percentage rate of change of 8%.
Therefore, the correct answer is:
B Exponential decay; 8%
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