Growth and decay question (1 Viewer)

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A colony of bacteria is growing exponentially and has doubled in size in 4 hours. How many hours will it take to increase by a factor of 7?


I missed out on class so I don't really understand, please help!

 

[word.]

um i think the formula goes something liek
P = Ae^(kt)
so let P be the current size, t be time in hrs

it doesn't matter what value of P you choose since it doubles,
you'll have to divide through and end up with the same result

so let's let P = 1 when t = 0,

so A = 1
P = e^(kt)

when t = 4, P = 2
2 = e^(4k)

k = (ln2)/4

consider t = 7 ..
P = e^(7k)
sub k in and solve for P

 

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Thanks mate

 

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The answer is 11.23 hours

But I don't know how to get it.

Is your last step incorrect?

 

[Riviet]

consider t = 7 ..
P = e^(7k)
sub k in and solve for P

We do not consider t=7, as we were not asked to find the size of the colony after 7 hours, rather we were asked to find how long it takes before the colony increases by a factor of 7.

Colony has increased by a factor of 7 when P=7x1=7

.'. 7=e^kt, where k=(ln2)/4

kt=ln7

t=(ln7)/k

=(ln7)
(ln2)/4

=11.23 hrs (2 decimal places)

 

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Thank you Riviet!