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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) ?

$p(t)=31(2)^{2t}$ $\newline$ 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 $(2,496)$ ?

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Simplify radical expressions with variables I

Full solution

Q.

p(t)=31(2)^{2t}

\newline

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)

?

Interpret Ordered Pair: To interpret the ordered pair $(2,496)$ , we need to understand that the first number represents the time in hours $(t)$ , and the second number represents the amount of bacteria in colony-forming units $(p)$ . We will check if the ordered pair $(2,496)$ fits the model $p(t)=31(2)^{2t}$ .
Substitute into Model: Substitute $t=2$ into the model to see if $p(2)$ equals $496$ . $\newline$ $p(2) = 31(2)^{(2*2)}$ $\newline$ $p(2) = 31(2)^4$ $\newline$ $p(2) = 31*16$ $\newline$ $p(2) = 496$
Final Interpretation: Since $p(2)$ equals $496$ , the ordered pair $(2,496)$ means that after $2$ hours of growth, there are $496$ colony-forming units of bacteria in the culture.

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