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A bacterial culture grows exponentially according to the function n(t)=n(e^rt), where n(t) is the quantity after "t" hours and "n" is the original quantity. If the culture grows from 20 bacteria to 45 bacteria in 2 days, how many bacteria will there be in 5 days?

Respuesta :

Answer:

There will be 152 bacteria in 5 days.

Step-by-step explanation:

We have that

[tex]n(t) = ne^{rt}[/tex]

We have that the original quantity is 20. So [tex]n = 20[/tex]

We also have that [tex]n(2) = 45[/tex]. This helps us find r.

[tex]n(t) = ne^{rt}[/tex]

[tex]45 = 20e^{2r}[/tex]

[tex]e^{2r} = 2.25[/tex]

Now we apply ln to both sides

[tex]2r = 0.811[/tex]

[tex]r = 0.405[/tex]

How many bacteria will there be in 5 days?

This is n(5)

[tex]n(t) = ne^{rt}[/tex]

[tex]n(5) = 20*e^{5*0.405} = 152[/tex]

There will be 152 bacteria in 5 days.

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