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Lucas is watching the bacterial population grow at a rate of 25% per year. The bacteria population originally started at 20 After 7 years hew many bactena will be present?

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Final answer:

Lucas is watching a bacterial population grow at a rate of 25% per year. Starting with 20 bacteria, after 7 years, using the exponential growth formula N = N0 * (1 + r)^t, Lucas will observe approximately 106 bacteria.

Step-by-step explanation:

Understanding Exponential Growth in Bacterial Populations

Lucas is observing a bacterial population that grows at a rate of 25% per year. The initial bacteria count is 20. To determine how many bacteria will be present after 7 years, we need to apply the formula for exponential growth:

N = N0 * (1 + r)^t

Where:

  • N = the number of bacteria after t years
  • N0 = initial number of bacteria
  • r = growth rate per period (in decimal form)
  • t = number of years

Using the given values:

  • N0 = 20
  • r = 0.25 (25% expressed as a decimal)
  • t = 7 years

Now we can calculate:

N = 20 * (1 + 0.25)^7

N = 20 * (1.25)^7

N = 20 * 5.322

N = approximately 106.44

Therefore, after 7 years, Lucas will see approximately 106 bacteria.

User Yogi Joshi
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