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A culture of bacteria has an initial population of 74000 bacteria and doubles every 3 hours. Using the formula
P
t
=
P
0
⋅
2
t
d
P
t
​
=P
0
​
⋅2
d
t
​

, where
P
t
P
t
​
is the population after t hours,
P
0
P
0
​
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?

Respuesta :

Using an exponential function, it is found that the population of bacteria in the culture after 13 hours is of 1,491,747.

An exponential function, with a doubling time of d, after t hours, is given by:

[tex]A(t) = A(0)(2)^{\frac{t}{d}}[/tex]

  • In which A(0) is the initial amount.

In this problem:

  • The doubling time is of 3 hours, hence [tex]d = 3[/tex].
  • The initial population is of 74000 bacteria, hence [tex]A(0) = 74000[/tex].

Then:

[tex]A(t) = A(0)(2)^{\frac{t}{d}}[/tex]

[tex]A(t) = 74000(2)^{\frac{t}{3}}[/tex]

After 13 hours:

[tex]A(13) = 74000(2)^{\frac{13}{3}} = 1491747[/tex]

The population of bacteria in the culture after 13 hours is of 1,491,747.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25958656

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