In an experiment to study the growth of bacteria, a medical student measured 5000 bacteria at time 0 and 8000 at time 10 minutes.

Question

Assuming that the number of bacteria grows exponentially, how many bacteria will be present after 30 minutes?

Answer 1

To determine the growth rate of the bacteria, we can use the formula for exponential growth:

N(t) = N0 * e^(rt)

where:
- N(t) is the number of bacteria at time t
- N0 is the initial number of bacteria (5000 at time 0)
- r is the growth rate
- t is the time in minutes

We are given that N0 = 5000 and N(10) = 8000. Substituting these values into the formula:

8000 = 5000 * e^(r*10)

Solving for r:

8000/5000 = e^(10r)
1.6 = e^(10r)
ln(1.6) = 10r
r = ln(1.6)/10
r ≈ 0.0464

Now that we have the growth rate, we can find the number of bacteria at 30 minutes (N(30)):

N(30) = 5000 * e^(0.0464*30)
N(30) ≈ 5000 * e^(1.392)
N(30) ≈ 5000 * 4.0156
N(30) ≈ 20078.14

Therefore, approximately 20,078 bacteria will be present after 30 minutes.