Question

Question 30 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?

Class X1 - Maths -Sequences and Series Page 193

Answer 1

Number of Bacteria present in the culture form GP whose 1st term (a) = 30 and common ratio (r) = 2.
∵ Tn = arⁿ⁻¹

so,
Bacteria present after 2nd hour(a₃) = ar² = 30(2)²= 120
Bacteria present after 4 hour(a₅) = ar⁴ = 30(2)⁴ = 480
Bacteria present after nth hour = arⁿ = 30(2)ⁿ

Answer 2

Given that,

The number of bacteria in a certain culture doubles every hour.

So, The number of bacteria after every hour will form a G.P.

First term a= 30

Common ratio r = 2

We need to calculate the number of bacteria at end of 2nd hour

Using G.P series

$r_{3}=ar^2$

Put the value into the formula

$r_{3}=30\times2^2$

$r_{3}=120$

We need to calculate the number of bacteria at end of 4th hour

Using G.P series

$r_{5}=ar^4$

Put the value into the formula

$r_{5}=30\times2^4$

$r_{5}=480$

We need to calculate the number of bacteria at end of nth hour

Using G.P series

$r_{n+1}=ar^n$

Put the value into the formula

$r_{n+1}=30\times2^n$

Hence, (I). The number of bacteria at end of 2nd hour is 120

(II). The number of bacteria at end of 4th hour is 480.

(III). The number of bacteria at end of nth hour is $30\times2^n$