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In a lab experiment, a population of 250 bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after 2 hours?

B=250(3)^(2)

B=3(250)^(2)

B=3(250)(250)

B=250(3)(3)(3)(3)

In a lab experiment, a population of $250$ bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after $2$ hours? $\newline$ $B=250(3)^{2}$ $\newline$ $B=3(250)^{2}$ $\newline$ $B=3(250)(250)$ $\newline$ $B=250(3)(3)(3)(3)$

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Write exponential functions: word problems

Full solution

Q. In a lab experiment, a population of

250

bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after

2

hours?

\newline

B=250(3)^{2}

\newline

B=3(250)^{2}

\newline

B=3(250)(250)

\newline

B=250(3)(3)(3)(3)

Define variables: Let's define the variables for the equation. We have an initial population of bacteria, which we'll call $P_0$ , and a growth rate, which we'll call $r$ . In this case, $P_0$ is $250$ and the bacteria triple every hour, so $r$ is $3$ . We want to find the population after $2$ hours, which we'll call $P_2$ .
General formula: The general formula for exponential growth is $P = P_0 \times r^t$ , where $P$ is the population at time $t$ , $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the time in hours. In this case, we want to find $P_2$ , so we will plug in $2$ for $t$ .
Substitute values: Substitute the known values into the equation: $P = 250 \times 3^2$ . This represents the population after $2$ hours, where $250$ is the initial population and $3^2$ is the growth factor after $2$ hours.
Calculate growth factor: Calculate the growth factor: $3^2 = 3 \times 3 = 9$ . This means the population will be $9$ times larger after $2$ hours.
Multiply initial population: Multiply the initial population by the growth factor to find the population after $2$ hours: $P_2 = 250 \times 9$ .
Perform multiplication: Perform the multiplication: $P_2 = 250 \times 9 = 2250$ . This is the number of bacteria in the population after $2$ hours.

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