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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) ?

p(t)=31(2)2tp(t)=31(2)^{2t}\newlineThe equation models pp, the amount of bacteria in colony-forming units in a bacteria culture after tt hours of growth. Which of the following statements is the best interpretation of the ordered pair (2,496)(2,496) ?

Full solution

Q. p(t)=31(2)2tp(t)=31(2)^{2t}\newlineThe equation models pp, the amount of bacteria in colony-forming units in a bacteria culture after tt hours of growth. Which of the following statements is the best interpretation of the ordered pair (2,496)(2,496) ?
  1. Interpret Ordered Pair: To interpret the ordered pair (2,496)(2,496), we need to understand that the first number represents the time in hours (t)(t), and the second number represents the amount of bacteria in colony-forming units (p)(p). We will check if the ordered pair (2,496)(2,496) fits the model p(t)=31(2)2tp(t)=31(2)^{2t}.
  2. Substitute into Model: Substitute t=2t=2 into the model to see if p(2)p(2) equals 496496.\newlinep(2)=31(2)(22)p(2) = 31(2)^{(2*2)}\newlinep(2)=31(2)4p(2) = 31(2)^4\newlinep(2)=3116p(2) = 31*16\newlinep(2)=496p(2) = 496
  3. Final Interpretation: Since p(2)p(2) equals 496496, the ordered pair (2,496)(2,496) means that after 22 hours of growth, there are 496496 colony-forming units of bacteria in the culture.

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