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A culture of bacteria has an initial population of 400 bacteria and doubles every 2 hours. Using the

formula Pt =

Po 2a, where P, is the population after t hours, Po is the initial population, t is the time

in hours and d is the doubling time, what is the population of bacteria in the culture after 13 hours, to the

nearest whole number?

A culture of bacteria has an initial population of 400 bacteria and doubles every 2 hours Using the formula Pt Po 2a where P is

Answer :

Answer:

36204

or as a exact number 25600*sqrt(2)

Step-by-step explanation:

To find the population of bacteria after 13 hours using the given formula Pt = Po × 2^(t/d), where:

Pt is the population after t hours,

Po is the initial population,

t is the time in hours, and

d is the doubling time (which is 2 hours in this case).

a = ratio of elapsed time/doubling time

We'll substitute the given values into the formula:

Pt = 400 × 2^(13/2)

Now, calculate the exponent:

13/2 = 6.5

Now, calculate 2^6.5 using a calculator which is 90.51 (this means that over 13 hours with a doubling time of 2 the population increases by 90.51 times)

Pt = 400 × 90.51 = 36204

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