find the percentage rate of change. P(t)3.5(0.91)^t

1 answer

To find the percentage rate of change for the function \( P(t) = 3.5(0.91)^t \), we need to look at the form of the function.

The expression \( 0.91 \) represents the growth factor, where a value less than 1 indicates a decrease. To find the percentage rate of change, we can calculate:

  1. Identifying the Rate of Change: The factor \( 0.91 \) implies that for each time period \( t \), the quantity \( P(t) \) is multiplied by \( 0.91 \), meaning it decreases by a certain percentage.

  2. Calculate the Decrease: The rate of change can be calculated as: \[ \text{Percentage Rate of Change} = (1 - 0.91) \times 100% \]

  3. Compute the Value: \[ \text{Percentage Rate of Change} = 0.09 \times 100% = 9% \]

Thus, the percentage rate of change of \( P(t) = 3.5(0.91)^t \) is -9%, indicating that the function decreases by 9% for each unit increase in \( t \).