204k views
1 vote
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?

1 Answer

4 votes

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
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories