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Title: Write the equation for the number N (this is your y) of bacteria as a function of time (in terms of ... Post by: 5seal on Apr 3, 2017 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. Title: Re: Write the equation for the number N (this is your y) of bacteria as a function of time (in ... Post by: bolbol on Apr 3, 2017 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. |