Question

A certain culture of bacteria grows at a rate proportional to its size. If the size doubles in 4 days,
the time required for the culture to increase to 10 times its original size is
(a) 15 (b) 13 (c) 12 (d) 20​

Answer 1

Given :  A certain culture of bacteria grows at a rate proportional to its size.  size doubles in 4 days,

To find : time required for the culture to increase to 10 times its original size

Solution:

$N_{t} = N_{0}e^{kt}$

k = growth Constant

size doubles in 4 days,

=>  $2N_{0} = N_{0}e^{k4}$

=>   $2 = e^{k4}$

=> ln 2 = 4k

=> k =  0.1732

=> $N_{t} = N_{0}e^{0.1732t}$

culture to increase to 10 times its original size

=>  $10N_{0} = N_{0}e^{0.1732t}$

=> ln 10 = 0.1732t

=> t = 13.29

approx 13 Days to become 10 times

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