A bacteria culture starts with 1000 bacteria. 2 hours later there are 1500 bacteria. How do you fin an exponential model for the size of the culture as function of time t in hours, and use the model to predict how many bacteria there will be after 2 days?

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Answer 1 · 2016-10-27T01:04:19

#P=16834112#

So and exponential growth or decay will fit the formula,

#P=P_"0"e^(r*t)#

where

#P= "current population at time t"#
#P_"0"= "starting population"#
#r= "rate of exponential growth/decay"#
#t= "time after start"#

so we sub in what we know

#1500=1000e^(r*2)#

#3/2=e^(r*2)#

#ln(3/2)=r*2#

#r=(ln(3)-ln(2))/2#

#r=0.20733#

so our population is modelled by,

#P=1000*e^((0.20733)*t)# , t hours after start

so 2 days is 48 hours so subbing in,

#P=1000*e^((0.20733)*(48))#

#P=16834112#