Pregunta
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Scientists measure a bacteria population and find that it is 10,000 . Five days later, they find that the population has doubled.
Which function ff could describe the bacteria population dd days after the scientists first measured it , assuming it grows
exponentally?

Ask by Fernandez Rojas. in the United States
Mar 23,2025

Solución de inteligencia artificial de Upstudy

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The bacteria population days after the initial measurement can be described by the function

Solución

  1. We know that the initial population is .
  2. Since the population doubles in 5 days, we have
  3. Assuming the population grows exponentially, we can write the function in the form
    where is the daily growth factor.
  4. We are given that . Dividing both sides by gives
  5. Solving for we get
  6. Substituting back into the function yields
Thus, the function that describes the bacteria population days after the initial measurement is

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Mind Expander

Did you know that bacterial populations can double in a matter of hours under the right conditions? This rapid growth is due to the simple cell division process called binary fission, where one bacterial cell splits into two. It’s fascinating to consider that in just a few days, the same population can increase from 10,000 to over a million, depending on the environment!
To better understand exponential growth, think about this: If you drop a single grain of rice on a chessboard and double it on each square, by the time you reach the last square, you’ll need more rice than is produced in the entire world! This highlights not only exponential growth but also how quickly things can get out of hand if left unchecked—much like bacteria in a nutrient-rich environment!

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