Question
find the percentage rate of change. P(t)3.5(0.91)^t
Answers
GPT-4o mini
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 \( t \).
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 \( t \).