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p(t)=31(2)^(2t) The equation models p, the amount of bacteria in colony-forming units in a bacteria culture after t hours of growth. Which of the following statements is the best interpretation of the ordered pair (2,496) ? Choose 1 answer: (A) There are 496 colony-forming units in the bacteria culture after 2 hours of growth. (B) There are 496 colony-forming units in the bacteria culture after 2 days of growth. (C) The number of colony-forming units in the bacteria culture reaches 496 after 2 generations. (D) The number of colony-forming units in the bacteria culture doubles every 496 minutes.

p(t)=31(2)2t p(t)=31(2)^{2 t} \newlineThe equation models p p , the amount of bacteria in colony-forming units in a bacteria culture after t t hours of growth. Which of the following statements is the best interpretation of the ordered pair (2,496) (2,496) ?\newlineChoose 11 answer:\newline(A) There are 496496 colony-forming units in the bacteria culture after 22 hours of growth.\newline(B) There are 496496 colony-forming units in the bacteria culture after 22 days of growth.\newline(C) The number of colony-forming units in the bacteria culture reaches 496496 after 22 generations.\newline(D) The number of colony-forming units in the bacteria culture doubles every 496496 minutes.

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Full solution

Q. p(t)=31(2)2t p(t)=31(2)^{2 t} \newlineThe equation models p p , the amount of bacteria in colony-forming units in a bacteria culture after t t hours of growth. Which of the following statements is the best interpretation of the ordered pair (2,496) (2,496) ?\newlineChoose 11 answer:\newline(A) There are 496496 colony-forming units in the bacteria culture after 22 hours of growth.\newline(B) There are 496496 colony-forming units in the bacteria culture after 22 days of growth.\newline(C) The number of colony-forming units in the bacteria culture reaches 496496 after 22 generations.\newline(D) The number of colony-forming units in the bacteria culture doubles every 496496 minutes.
  1. Plug in t=2t=2: Plug in t=2t=2 into the equation to check if p(2)p(2) equals 496496.
    p(2)=31(2)(2∗2)p(2)=31(2)^{(2*2)}
    p(2)=31(2)4p(2)=31(2)^4
    p(2)=31∗16p(2)=31*16
    p(2)=496p(2)=496
  2. Calculate p(2)p(2): Since p(2)=496p(2) = 496, the ordered pair (2,496)(2,496) means there are 496496 colony-forming units after 22 hours of growth.

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