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A 700-liter tank is initially full of water and is drained at a rate of 12.5 liters per minute. Which of these is true given that the function n models the number of liters of water in the tank after m minutes? Select two that apply.

A.
n(0) = 0

B.
n(56) = 0

C.
n(0) = 56

D.
n(0) = 700

E.
n(700) = 0

F.
n(56) = 700

1 answer

To model the number of liters of water in the tank after \( m \) minutes, we can use the function:

\[ n(m) = 700 - 12.5m \]

This represents the initial amount of water (700 liters) minus the water drained after \( m \) minutes at a rate of 12.5 liters per minute.

Now, let's analyze the options:

A. \( n(0) = 0 \)

  • False. At \( m = 0 \), \( n(0) = 700 - 12.5(0) = 700 \).

B. \( n(56) = 0 \)

  • True. At \( m = 56 \), \( n(56) = 700 - 12.5(56) = 700 - 700 = 0 \).

C. \( n(0) = 56 \)

  • False. As calculated above, \( n(0) = 700 \).

D. \( n(0) = 700 \)

  • True. As calculated, \( n(0) = 700 \).

E. \( n(700) = 0 \)

  • False. At \( m = 700 \), \( n(700) = 700 - 12.5(700) = 700 - 8750 = -8150\) (which is not applicable since the tank cannot have negative water).

F. \( n(56) = 700 \)

  • False. As calculated, \( n(56) = 0 \).

Thus, the true statements are:

  • B. \( n(56) = 0 \)
  • D. \( n(0) = 700 \)