We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
71
3
avatar+177 

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+104969 
+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+104969 
0

THX, guest   !!!

 

 

 

cool cool cool

CPhill  Oct 15, 2019

16 Online Users

avatar