The bacteria in a certain culture double every 7.5 hours. The culture has 6,500 bacteria at the start.

How many bacteria will the culture contain after 3 hours?

Select one:

number = 6500(2)^(t/7.5) where t is in hours

at t=3
number = 6500(2)^3/7.5 = 6500(2)^.4
= appr 8579

To find out how many bacteria the culture will contain after 3 hours, we need to use the formula for exponential growth:

N = N0 * 2^(t/d)

Where:
N = final number of bacteria
N0 = initial number of bacteria
t = time (in hours)
d = doubling time (in hours)

In this case:
N0 = 6,500 bacteria
t = 3 hours
d = 7.5 hours

Substituting these values into the formula:

N = 6,500 * 2^(3/7.5)

Calculating 2^(3/7.5):

2^(3/7.5) ≈ 1.272

N ≈ 6,500 * 1.272

N ≈ 8,268

Therefore, the culture will contain approximately 8,268 bacteria after 3 hours.

To determine the number of bacteria in the culture after 3 hours, we can use the formula for exponential growth. The formula is:

N = N₀ * (2^(t/g))

Where:
N = Final number of bacteria
N₀ = Initial number of bacteria
t = Time in hours
g = Time it takes for the population to double

Given that the bacteria double every 7.5 hours, we can plug in the values into the formula:

N = 6,500 * (2^(3/7.5))

Now, let's calculate the result.

N = 6,500 * (2^0.4)
N ≈ 6,500 * 1.316074

Therefore, the culture will contain approximately 8,548 bacteria after 3 hours.