Lets say we have a sample of 100 bacteria in a lab that doubles every 30 minutes. What formula would we apply here and how many bacteria would you expect to find in 35 minutes?

n = 100 e^(kt)

200 = 100 e^(30 k)
e^(30k) = 2
30 k = ln 2
k = .0231
so
n = 100 e^(.0231 t)
if t = 35
n(35min) = 100 e^(.0231*35)
= 224

To calculate the number of bacteria after a certain amount of time, we can use the formula:

N = N₀ * (2^(t / t₀))

Where:
N is the final number of bacteria
N₀ is the initial number of bacteria
t is the total time elapsed
t₀ is the doubling time (in this case, 30 minutes)

In this scenario, the initial number of bacteria (N₀) is 100 and the time elapsed (t) is 35 minutes. The doubling time (t₀) remains at 30 minutes.

So, to find the number of bacteria after 35 minutes, we plug these values into the formula:

N = 100 * (2^(35 / 30))

Calculating the exponent first:
35 / 30 = 1.1667

Substituting this back into the formula:
N ≈ 100 * (2^1.1667)

Using a calculator or computer, we can evaluate 2^1.1667 ≈ 2.682

Finally, multiplying this with the initial number of bacteria:
N ≈ 100 * 2.682 ≈ 268.2

Therefore, you would expect to find approximately 268 bacteria after 35 minutes.