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# help plz

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A bacterial culture is growing exponentially, and its mass increases from 2 mg to 5 mg in 30 hours. Find the mass of the culture after 25 hours.

Oct 15, 2019

#1
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We have the following  equation

M  =  ae^(kt)

Where M is the mass after t hours

a  = the beginning mass

k  is the growth constant

We need to find k   thusly

5  = 2e^(k 30)       divide both sides by  2

2.5  =  e^(30k)       take the Ln  on both sides

Ln 2.5  =  Ln e^(30k)         and we can write

Ln 2.5  =  30k   * Ln e           [Ln e = 1....so we can ignore this ]

Ln 2.5 =  30 k       divide both sides by  30

Ln (2.5) /30 = k

After 25 hours we have that

M  = 2e^(Ln (2.5)/30* 25)   ≈  4.29  mg   Oct 15, 2019
edited by CPhill  Oct 15, 2019
#2
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Here is a shorter way:

5/2 =2.5 - total growth after 30 hours.

2.5^(1/30) =1.03101424786... growth rate per hour.

1.03101424786^25 =2.145935547,,, x 2 =~ 4.29 mg - exponential  growth after 25 hours.

Oct 15, 2019
#3
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THX, guest   !!!   CPhill  Oct 15, 2019