To determine whether the function \( P(t) = 8.5(0.92)^t \) represents exponential growth or decay, we need to 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, the function represents exponential decay.
Since \( 0.92 < 1 \), the function represents exponential decay.
Next, we can find the percentage rate of change. The general form for an exponential decay function is \( P(t) = P_0(1 - r)^t \), where \( r \) is the decay rate.
In our function, we can see that:
\[ P(t) = 8.5(0.92)^t \]
Here, \( 0.92 = 1 - r \), which implies:
\[ r = 1 - 0.92 = 0.08 \]
To express this as a percentage:
\[ r = 0.08 \times 100% = 8% \]
Putting this all together:
- The function is exponential decay.
- The percentage rate of change is 8%.
Thus, the correct answer is:
B. Exponential decay; 8%.
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