Question

While doing experiment on Covid virus culture, it was found that the number of viruses in that culture doubles every hour. If there were 40 viruses present in the culture originally, how many viruses will be present at the end of 3^rd hour, 5^th hour and nth hour?
1. 320 ; 1280 ; 20 × 4ⁿ
2. 320 ; 1280 ; 40 × 2n
3. 420 ; 1480 ; 20 × 4n
4. 420 ; 1480 ; 40 × 2n

Answer 1

Correct Answer - Option 2 : 320 ; 1280 ; 40 × 2n

Given∶

40 viruses were present in the culture originally. 

Formula Used∶

Concept of general term of a G.P, a_n = a r^n-1

Calculation∶

Clearly, number of viruses at the end of different hours forms a G.P. with first term a = 40 and common ratio r = 2

Number of virus present at the 3^rd hour,

⇒ 4^th term of the G.P. with first term a = 40 and common ratio r = 2

⇒ ar³ = 40 

× 2³ = 320

Number of virus present at the end of 5^th hour,

⇒ 6^th term of the G.P. with first term a = 30 and common ratio r = 2

⇒ ar⁵ = 40 

× 2⁵ = 1280

Number of virus present at the end of nth hour,

⇒ (n + 1)^th term of the G.P. with first term a = 30 and common ratio, r = 2

⇒ arⁿ = 40 

× 2ⁿ

∴ 320, 1280 and 40 

× 2ⁿ are the number of virus present at the end of 3rd, 5th and nth hour.