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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
avatar+106536 
+3

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

 

 

cool cool  cool

 Oct 15, 2019
edited by CPhill  Oct 15, 2019
 #2
avatar
+1

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
avatar+106536 
0

THX, guest   !!!

 

 

 

cool cool cool

CPhill  Oct 15, 2019

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