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The bacteria in a Petri dish culture are self-duplicating at a rapid pace.
The relationship between the elapsed time
t, in minutes, and the number of bacteria,
B(t), in the Petri dish is modeled by the following function.

B(t)=10*2^((t)/( 12))
How many bacteria will make up the culture after 120 minutes?
Round your answer, if necessary, to the nearest hundredth.
bacteria

The bacteria in a Petri dish culture are self-duplicating at a rapid pace. $\newline$ The relationship between the elapsed time $t$ , in minutes, and the number of bacteria, $B(t)$ , in the Petri dish is modeled by the following function. $\newline$ $B(t)=10 \cdot 2^{\frac{t}{12}}$ $\newline$ How many bacteria will make up the culture after $120$ minutes? $\newline$ Round your answer, if necessary, to the nearest hundredth. $\newline$ bacteria

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Weighted averages: word problems

Full solution

Q. The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

\newline

The relationship between the elapsed time

t

, in minutes, and the number of bacteria,

B(t)

, in the Petri dish is modeled by the following function.

\newline

B(t)=10 \cdot 2^{\frac{t}{12}}

\newline

How many bacteria will make up the culture after

120

minutes?

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

bacteria

Identify function: Identify the given function that models the number of bacteria over time. $\newline$ The function is $B(t) = 10 \cdot 2^{\frac{t}{12}}$ .
Substitute time: Substitute the given time $t = 120$ minutes into the function to find $B(120)$ . $B(120) = 10 \times 2^{(120/12)}$ .
Simplify exponent: Simplify the exponent by dividing $120$ by $12$ . $\newline$ $\frac{120}{12} = 10$ .
Calculate power: Calculate $2$ raised to the power of $10$ . $\newline$ $2^{10} = 1024$ .
Multiply result: Multiply the result from Step $4$ by $10$ to find the number of bacteria after $120$ minutes. $\newline$ $B(120) = 10 \times 1024$ .
Perform multiplication: Perform the multiplication to get the final result. $B(120) = 10 \times 1024 = 10240$ .

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