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,

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

$P=16834112$