A scientist is studying the population of bacteria in a laboratory. At the beginning of the experiment, there are $3.0 \times 10^5$ bacteria. After 3 hours, the population grows to $4.2 \times 10^3$ times its original size. What is the new population of bacteria expressed in scientific notation?
A. $1.26 \times 10^{11}$
B. $1.26 \times 10^9$
C. $1.26 \times 10^8$
D. $1.26 \times 10^{10}$
Answer (2)
Multiply the initial population by the growth factor: ( 3.0 × 1 0 5 ) × ( 4.2 × 1 0 3 ) .
Multiply the numbers: 3.0 × 4.2 = 12.6 .
Multiply the powers of 10: 1 0 5 × 1 0 3 = 1 0 8 .
Express the result in scientific notation: 12.6 × 1 0 8 = 1.26 × 1 0 9 . The new population is 1.26 × 1 0 9 .
Explanation
Understanding the Problem We are given that the initial population of bacteria is 3.0 × 1 0 5 . The population grows to 4.2 × 1 0 3 times its original size. We need to find the new population of bacteria in scientific notation.
Setting up the Calculation To find the new population, we multiply the initial population by the growth factor:
New population = Initial population × Growth factor
New population = ( 3.0 × 1 0 5 ) × ( 4.2 × 1 0 3 )
Multiplying the Numbers First, let's multiply the numbers:
3.0 × 4.2 = 12.6
Multiplying the Powers of 10 Next, let's multiply the powers of 10:
1 0 5 × 1 0 3 = 1 0 5 + 3 = 1 0 8
Combining the Results Now, combine the results:
New population = 12.6 × 1 0 8
Expressing in Scientific Notation To express the result in scientific notation, we need to write 12.6 as 1.26 × 1 0 1 . So,
12.6 × 1 0 8 = 1.26 × 1 0 1 × 1 0 8 = 1.26 × 1 0 1 + 8 = 1.26 × 1 0 9
Therefore, the new population of bacteria is 1.26 × 1 0 9 .
Examples
Understanding bacterial growth is crucial in many fields, such as medicine and environmental science. For instance, if you're studying how quickly a bacterial infection spreads, knowing the growth rate helps predict the severity and timing of symptoms. Similarly, in environmental studies, understanding how bacteria break down pollutants can help in designing effective bioremediation strategies. This problem demonstrates a fundamental calculation used to model such growth, allowing scientists to make informed decisions and predictions.
The new population of bacteria, after growing from an initial amount of 3.0 × 1 0 5 to 4.2 × 1 0 3 times its original size, is 1.26 × 1 0 9 . The answer chosen from the provided options is B. 1.26 × 1 0 9 .
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