The number of bacteria in a culture initially and after 10 hours can be given by the points (0, 250) and (10, 540), where x is the number of hours and y is the number of bacteria. Use the 2 points to write the model y=ae^bx. How Do I Solve This Problem?

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Answer 1 · 2018-03-30T04:51:58

Exponenial model of bacteria growth is #y=250e^(0.0770108 x)#

At time #x=0#, the number of bacteria is #y_0=a=250#

At time #x=10# hour, the number of bacteria is #y_10=540#

The growth model is #y=ae^(bx)# , where #a# is number

of bacteria initially , #y#, the number of bacteria after time

#x# hours and #b# , the exponentially growth constant of

bacteria. Initially # y_0=250=250*e^(b*0)= 250;(1) [e^0=1]#

At time #x=10#, hour # y_10=540=250*e^(b*10) ; (2)#

Dividing equation (2) by equation (1) we get,

#540/250= (cancel(250)*e^(b*10))/cancel250# or

#2.16=e^(10b)# taking natural log on both sides , we get,

#ln (2.16) =10b *ln e or 10b = ln (2.16) ; [ln e=1]#

#b= ln(2.16)/10 or b=0.0770108# , So the exponenial

model of bacteria growth is #y=250e^(0.0770108 x)# [Ans]