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.