We can Notice that : Number of Cells growth is a Geometric Sequence
That is : 1 , 2 , 4 , 8 , 16. . . . .
We know that : nth term in a Geometric Sequence is = a.rⁿ⁻¹
where a is the first term
r is the common ratio, which is given by ratio of 2nd term to 1st term
For the above Sequence, a = 1 and r = 2
Given : nth term over 1000
⇒ 1.2ⁿ⁻¹ = 1024
⇒ 2ⁿ⁻¹ = 2¹⁰
⇒ n - 1 = 10
⇒ n = 11
We can Notice that : Number of Hours is a Arithmetic Sequence
That is : 0 , 3 , 6 , 9 , 12
We know that : nth term in a Arithmetic Sequence is = a + (n - 1)d
where a is the first term
r is the common difference, which is given by difference between 2nd term and 1st term
For the above Sequence, a = 0 and r = 3 - 0 = 3
we need to find the number of hours, which is when : n = 11
⇒ 0 + (11 - 1)3
⇒ 10(3)
⇒ 30
⇒ It will take 30 hours to have over 1000 bacteria
