Question

Can someone help me?

Answer 1

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