Question

The mass of a bacteria culture doubles every four days. If the initial sample is 5mg: a) how much will you have after one week (7 days). B) how long does it take to reach a mass of 320mg?

Answer 1

a) 16.82 mg

b) 24 days

Explanation:

Formula for exponential growth is given as:

`A=A_0b^{(t)/(c)}`

Where A is the final population

`A_0` is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, We are given the following:

`A_0` = 5 mg

b = 2 (Given because it doubles)

c = 4 days

a) A = ?

Using the formula:

`A=5 * 2^{(7)/(4)}\\\Rightarrow A=5 * 2^(1.75) \\\Rightarrow A = \bold{16.82\ mg}`

b) Given

A = 320 mg

t = ?

Using the above formula again:

`320 = 5 * 2^{(t)/(4)}\\\Rightarrow \frac{320} 5= 2^{(t)/(4)}\\\Rightarrow 2^{(t)/(4)} = 64\\\Rightarrow 2^{(t)/(4)} = 2^6\\\Rightarrow (t)/(4) = 6\\\Rightarrow t = 6 * 4\\\Rightarrow \bold{t = 24\ days}`

So, the answers are:

a) 16.82 mg

b) 24 days