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A bacteria population grows such that growth rate is proportional to population. At t=0 there are 100000 bacteria. At 48 hours there are 300000. How many bacteria will there be at t=72 hours?

Answer 1

Madelyn Anderson

Population after #72# hrs is #519615# after rounding up.

General form of equation for natural growth [exponential] is

#P=Ce^[kt]#. So given that at time #=0#, population is 100,000 we have....

#100,000 =Ce^[k[0]# and since #e^[k[0]#=1, then #C=100,000# and so

#P=100,000e^[kt#. And thus , when the population is #300,000# at time #t=48#

#300,000=100,000e^[48k#, solving this for #k#

ln #3= 48k,# ie #k=ln3/48#, which is #0.022889# to six decimal places.

This now gives #P=100,000e^[.022889t]#...........#[1]#, and substituting #t=72# into #[1]#

#P=100,000e^[1.647918]# which gives #P=519615#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.