Let's analyze the given equation \( m(p) = 20(2)^p \).
- Understanding how \( m \) changes with \( p \):
- The equation \( m(p) = 20(2)^p \) is an exponential function where the base is 2.
- As \( p \) (the number of people who pass on the money) increases, \( m \) increases exponentially because \( 2^p \) grows very rapidly.
- Therefore, as \( p \) increases, \( m \) increases quickly.
It is accurate to say:
- As \( p \) increases, \( m \) increases quickly at first and then continues to increase rapidly.
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Domain:
- The variable \( p \) represents the number of people who choose to pass the money on. Since it cannot be negative, the smallest value \( p \) can take is 0 (when the first person is asked).
- Thus, the domain is \( p \geq 0 \).
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Range:
- The minimum value of \( m \) occurs when \( p = 0\): \[ m(0) = 20(2)^0 = 20. \]
- As \( p \) increases, \( m \) will also increase without bound, so the range of \( m \) is \( m \geq 20 \).
Based on this analysis, we can conclude:
- The statement that is true about the equation is: As \( p \) increases, \( m \) increases quickly at first and then slowly.
For the other statements about the domain and range:
- The domain (p-values) is \( p \geq 0 \).
- The range (m-values) is \( m \geq 20 \).
Thus, the complete true statements are:
- As \( p \) increases, \( m \) increases quickly at first and then slowly.
- The range (m-values) includes the values \( m \geq 20 \).