Question

How long does it take the culture to double its mass if a bacterial culture which is growing exponentially increases from 5 g to 7 g in 11 hours?

Answer 1

This is an example of a exponential function.

The form is always `N=B*g^t`
Where
`N`=new situation
`B`=begin
`g`=growth factor
`t`=time units

Now we fill in what we know:
`N=B*g^t->7=5*g^11->g^11=7//5=1.4`
Now grow factor `g` is the 11th root of `1.4`

You can do this on your calculator by `"1.4^(1/11)"` or
`1.4^(1/11)=1.03106...`

The growth factor can then be used in the equation:
`N=B*g^t->10=5*1.03106...^t->1.03106...^t=2`

From here on there are two ways to go:

(1) put this equation in your GC as Y1= and intersect with Y2=2

(2) Use logarithms:

`1.03106...^t=2->log 1.03106...^t=log2->`
`t*log1.03106...=log2->t=log2/log1.03106~~22.3`

Answer : a bit more than 22 hours. This is the doubling time from any start situation.