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Aleonysh [2.5K]
3 years ago
10

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?
Mathematics
1 answer:
maks197457 [2]3 years ago
6 0

Answer:

a) 16.82 mg

b) 24 days

Step-by-step explanation:

Formula for exponential growth is given as:

A=A_0b^{\frac{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 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}

b) Given

A = 320 mg

t = ?

Using the above formula again:

320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}

So, the answers are:

a) 16.82 mg

b) 24 days

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