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Exponential Growth and Decay: Word Problem

If the number of bacteria in a colony doubles every 203 minutes and there is currently a population of 40 bacteria, what will the population be 812 minutes from now?

Answer :

Final answer:

The population of bacteria will be 640 after 812 minutes.

Explanation:

To find the population after 812 minutes, we can use the formula for exponential growth:

P = P0 * (2^(t/d))

Where:

  • P is the final population
  • P0 is the initial population
  • t is the time elapsed
  • d is the doubling time

In this case, the initial population (P0) is 40 bacteria, the time elapsed (t) is 812 minutes, and the doubling time (d) is 203 minutes.

Substituting these values into the formula:

P = 40 * (2^(812/203))

Calculating the exponent:

P = 40 * (2^4)

P = 40 * 16

P = 640

Therefore, the population will be 640 bacteria 812 minutes from now.

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Final answer:

The population of bacteria will be 640 after 812 minutes.

Explanation:

To find the population after 812 minutes, we can use the formula for exponential growth:

P = P0 * (2^(t/d))

Where:

  • P is the final population
  • P0 is the initial population
  • t is the time elapsed
  • d is the doubling time

In this case, the initial population (P0) is 40 bacteria, the time elapsed (t) is 812 minutes, and the doubling time (d) is 203 minutes.

Substituting these values into the formula:

P = 40 * (2^(812/203))

Calculating the exponent:

P = 40 * (2^4)

P = 40 * 16

P = 640

Therefore, the population will be 640 bacteria 812 minutes from now.

Learn more about exponential growth and decay: word problems here:

https://brainly.com/question/28142560

#SPJ14