To analyze the exponential equation \( m(p) = 20(2)^p \), let's break down the components:
1. **Understanding the context**:
- \( m \) represents the money available after passing it on to the next person.
- \( p \) represents the number of people who choose to pass the money on.
2. **Examining the equation**:
- The equation starts with an initial value of $20 when \( p = 0 \).
- As \( p \) increases, the value of \( m \) increases because the term \( (2)^p \) grows exponentially.
3. **Range of the function**:
- When \( p = 0 \), \( m(0) = 20(2^0) = 20 \).
- As \( p \) increases, \( m \) continues to increase without bound, so the range of \( m \) is \( m \geq 20 \). Therefore, the statement "The range (m-values) includes the values \( m \geq 20 \)" is true.
4. **Behavior of the function**:
- As \( p \) increases, \( m(p) \) increases quickly at first due to the exponential nature of the function and then continues to grow quickly but at a larger scale. This means it does not decrease; it only increases.
5. **Domain of the function**:
- The domain of the function is not restricted to \( p \geq 20 \); instead, \( p \) can take on any non-negative integer value (typically \( p \geq 0 \) in this context).
### Conclusion:
The only true statement regarding the exponential equation \( m(p) = 20(2)^p \) is:
**The range (m-values) includes the values \( m \geq 20 \).**