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In a lab experiment, 30 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 7 hours. How many bacteria would there be after 16 hours, to the nearest whole number?
Answer: ◻

In a lab experiment, $30$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $7$ hours. How many bacteria would there be after $16$ hours, to the nearest whole number? $\newline$ Answer: ◻

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Multi-step word problems

Full solution

Q. In a lab experiment,

30

bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every

7

hours. How many bacteria would there be after

16

hours, to the nearest whole number?

\newline

Answer: ◻

Calculate Doubling Times: Figure out how many times the bacteria will double in $16$ hours. Since they double every $7$ hours, divide $16$ by $7$ . $\newline$ $\frac{16}{7} = 2$ with a remainder, so the bacteria will double $2$ times completely.
Calculate Bacteria After Doubling: Calculate the number of bacteria after the full doubling periods. Start with $30$ and double it twice. $30 \times 2 \times 2 = 120$ .
Estimate Growth in Remaining Hours: Deal with the remainder hours. There are $2$ hours left ( $16 - 2\times7 = 2$ ). In $2$ hours, the bacteria won't fully double, but they will grow. Since $2$ hours is about $\frac{2}{7}$ of the full $7$ -hour period, we can estimate the growth by multiplying the current amount by $\frac{2}{7}$ . $\newline$ $120 \times \left(\frac{2}{7}\right) = 34.2857$ , but we need to add this to the original $120$ , not multiply.

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