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A. Express the total population of bacteria from both samples in scientific notation. (Correct answer with a detailed solution will earn 2 points)
Solution:
Convert the populations to a common exponent:
First sample: 3.2 x 10⁷ bacteria
Second sample: 5.4 x 10⁶ bacteria = 0.54 x 10⁷ bacteria
Add the populations:
Total population = (3.2 x 10⁷) + (0.54 x 10⁷) = 3.74 x 10⁷ bacteria
Therefore, the total population of bacteria from both samples is 3.74 x 10⁷ bacteria.
B. During an experiment, the biologist found that the bacteria population in the first sample increased by a factor of 2.5 x 10³. Calculate the new population of bacteria in the first sample and express the result in scientific notation. (Correct answer with a detailed solution will earn 2 points)
Solution:
Multiply the original population by the factor of increase:
New population = (3.2 x 10⁷) * (2.5 x 10³)
Multiply the coefficients and add the exponents:
New population = (3.2 * 2.5) x 10⁽⁷⁺³⁾ = 8 x 10¹⁰ bacteria
Therefore, the new population of bacteria in the first sample is 8 x 10¹⁰ bacteria.
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