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Home Q & A Board Science-Related Homework Help Mathematics
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5seal 5seal
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Posts: 147
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7 years ago
A bacterial sample contains 2950 bacteria and grows at a rate of 6.05% per hour. Assuming that the bacteria grow exponentially,

a) Write the equation for the number N (this is your y) of bacteria  as a function of time (in terms of t)

b) Find the time for the sample to grow to 12 000 bacteria.
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#1
Staff Member
7 years ago
a) Exponential growth means that
n(t)=n0ert

n(t)= population at time t
n0=initial size of the population
r=relative rate of growth (expressed as proportion of the population)
t= time

n0=2950 bacteria
r=0.0605

n(t)=2950e0.0605t

where t is measured in hours

b) We set n(t) = 12 000 and solve the resulting exponential equation for t:

12000=2950e0.0605t
Divide by 2950

4.0678=e0.0605t
Take ln of each side and solve for t

ln4.0678=0.0605t

t=ln4.0678/0.0605
t=23.19 hr

The bacteria level reaches 12,000 in about 23.2 hours.
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