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A colony of $150$ bacteria doubles in size every $48$ hours. What will the population be $144$ hours from now?

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Exponential growth and decay: word problems

Full solution

Q. A colony of

150

bacteria doubles in size every

48

hours. What will the population be

144

hours from now?

Identify Parameters: Identify initial amount, time, and doubling period. Initial amount = $150$ Total time = $144$ hours Doubling period = $48$ hours
Calculate Doubling Periods: Calculate the number of doubling periods in $144$ hours. Number of doubling periods = $\frac{144}{48} = 3$
Use Exponential Growth Formula: Use the formula for exponential growth: $P = P_0 \times 2^n$ $\newline$ Where $P_0 = 150$ and $n = 3$
Calculate Final Population: Calculate the population after $3$ doubling periods. $\newline$ $P = 150 \times 2^3$ $\newline$ $P = 150 \times 8$ $\newline$ $P = 1200$

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