Login/Sign Up
Home » 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 2nd hour, 4th hour and nth hour?
CBSE | Class 11 | Exercise 9.3 | Maths | NCERT | Sequences and Series
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?

Given, the quantity of bacteria copies each hour. Henceforth, the quantity of bacteria after consistently will frame a G.P.

Here we have,

    \[a\text{ }=\text{ }30\text{ }and\text{ }r\text{ }=\text{ }2\]

Thus,

    \[{{a}_{3}}~=~a{{r}^{2}}~=\text{ }\left( 30 \right)\text{ }{{\left( 2 \right)}^{2}}~=\text{ }120\]

In this manner, the quantity of bacteria toward the finish of

    \[{{2}^{nd}}~hour\text{ }will\text{ }be\text{ }120.\]

Also,

    \[{{a}_{5}}~=~a{{r}^{4}}~=\text{ }\left( 30 \right)\text{ }{{\left( 2 \right)}^{4}}~=\text{ }480\]

The quantity of bacteria toward the finish of

    \[{{4}^{th}}~hour\text{ }will\text{ }be\text{ }480.\]

    \[{{a}_{n}}_{~+1~}=~a{{r}^{n}}~=\text{ }\left( 30 \right)\text{ }{{2}^{n}}\]

In this manner, the quantity of bacteria toward the finish of

    \[{{n}^{th}}~hour\text{ }will\text{ }be\text{ }30{{\left( 2 \right)}^{n}}.\]

i

More Material