The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^nd hour, 4^th hour and n^th hour?

Open in App

Solution

It is given that the number of bacteria doubles every hour. Therefore, the number of bacteria after every hour will form a G.P.

Here, a = 30 and r = 2

∴ a₃ = ar² = (30) (2)² = 120

Therefore, the number of bacteria at the end of 2^nd hour will be 120.

a₅ = ar⁴ = (30) (2)⁴ = 480

The number of bacteria at the end of 4^th hour will be 480.

a_n₊₁= arⁿ = (30) 2ⁿ

Thus, number of bacteria at the end of n^th hour will be 30(2)ⁿ.

Suggest Corrections

Similar questions

Q. The number of bacteria in a certain culture doubles every hour. If there were

30

bacteria present in the culture originally, how many bacteria will be present at the end of

2^{n d}

hour

4^{t h}

hour and

n^{t h}

hour?

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture origi nally, how many bacteria will be present at the end of $2^{n d} h o u r, 4^{t h} h o u r a n d n^{t h}$ hour.

Q. The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2 nd hour, 4 th hour and n th hour?

Q. The number of bacteria in a certain culture doubles every hour. If there were

30

bacteria present in the culture initially, how many bacteria will be present at the end of

14^{t h}

hour?

A school divided to conduct a seminar for small children highlighting the importance of keeping cleaniness at home and at workplace and also personal hygenic to keep bacteria at by as excessive increase in the number of certain bacteria in a certain culture double every hour. If there were 30 bacteria, present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour? What value is being highlighted in the seminar?

Join BYJU'S Learning Program

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour?

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^nd hour, 4^th hour and n^th hour?