Hi everyone,

I've asked this question before and was given understandable solutions. However, I would like to know whether the below ways works for this type of problem:-

A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^4, what was the number in the population 1 hour later.

A)2(10^4)

B)6(10^4)

C)(2^6)(10^4)

D)(10^6)(10^4)

E)(10^4)^6

The answer is C.

Can I solve it this way?

Time Elapsed Population

Initially(Now) 10^4

10 minutes 10^4 + 10^4 = 10^4(2)

20 minutes (2)10^4 + (2)10^4 = got stuck

30 minutes

40 minutes

50 minutes

60 minutes

For ex: Double 5 = 2(5) = 10 or 5+5=10.

So in this case, I can use 2(10^4) which the answer will lead to (2^6)(10^4) but I would like to try adding it. Is it possible? Can anyone show me how?

I hope you guys understand what I'm trying to say here. I don't how to put it in right words.

Thank you.

## Population - OG-2nd Edition

##### This topic has expert replies

- vk_vinayak
- Legendary Member
**Posts:**502**Joined:**03 Jun 2008**Thanked**: 99 times**Followed by:**21 members

I am showing the calculation you left off:shanice wrote:Hi everyone,

I've asked this question before and was given understandable solutions. However, I would like to know whether the below ways works for this type of problem:-

A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^4, what was the number in the population 1 hour later.

A)2(10^4)

B)6(10^4)

C)(2^6)(10^4)

D)(10^6)(10^4)

E)(10^4)^6

The answer is C.

Can I solve it this way?

Time Elapsed Population

Initially(Now) 10^4

10 minutes 10^4 + 10^4 = 10^4(2)

20 minutes (2)10^4 + (2)10^4 = got stuck

30 minutes

40 minutes

50 minutes

60 minutes

For ex: Double 5 = 2(5) = 10 or 5+5=10.

So in this case, I can use 2(10^4) which the answer will lead to (2^6)(10^4) but I would like to try adding it. Is it possible? Can anyone show me how?

I hope you guys understand what I'm trying to say here. I don't how to put it in right words.

Thank you.

Time Elapsed Population

Initially(Now) 10^4

10 minutes 10^4 + 10^4 = 10^4(2)

20 minutes (2)10^4 + (2)10^4 => 2 (10^4 + 10^4) => 2 (2)(10^4) => 2^2 (10^4)

30 minutes 2^2 (10^4) + 2^2 (10^4) => 2^2 (10^4 + 10^4) => 2^2 (2) 10^4 => 2^3 (10^4)

40 minutes

50 minutes

60 minutes

You can see that 2 (10^4) is common in all these, and the power of 2 is increasing with each 10 minutes.

The power of 2:

Initially 0, After 10 minutes => 1, After 20 minutes =>2, After 30 minutes =>3, ... so after 60 minutes, the power of 2 will be 6.

Therefore ans is : 2^6 (10^4)

- VK

I will (Learn. Recognize. Apply)

I will (Learn. Recognize. Apply)

- niketdoshi123
- Master | Next Rank: 500 Posts
**Posts:**210**Joined:**08 Mar 2012**Thanked**: 62 times**Followed by:**3 members

The best way to solve this question is to simply multiply '2' 6 times to 10^4.shanice wrote:Hi everyone,

I've asked this question before and was given understandable solutions. However, I would like to know whether the below ways works for this type of problem:-

A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^4, what was the number in the population 1 hour later.

A)2(10^4)

B)6(10^4)

C)(2^6)(10^4)

D)(10^6)(10^4)

E)(10^4)^6

The answer is C.

Can I solve it this way?

Time Elapsed Population

Initially(Now) 10^4

10 minutes 10^4 + 10^4 = 10^4(2)

20 minutes (2)10^4 + (2)10^4 = got stuck

30 minutes

40 minutes

50 minutes

60 minutes

For ex: Double 5 = 2(5) = 10 or 5+5=10.

So in this case, I can use 2(10^4) which the answer will lead to (2^6)(10^4) but I would like to try adding it. Is it possible? Can anyone show me how?

I hope you guys understand what I'm trying to say here. I don't how to put it in right words.

Thank you.

However if you want to solve it by adding

Time Elapsed________________Population

Initially(Now)________________10^4

10 minutes________________10^4 + 10^4 = 10^4(2)

20 minutes________________(2)10^4 + (2)10^4 = (4)*10^4=(2^2)*10^4

30 minutes________________(4)10^4 + (4)10^4 = (8)*10^4=(2^3)*10^4

40 minutes________________(8)10^4 + (8)10^4 = (16)*10^4=(2^4)*10^4

50 minutes________________(16)10^4 + (16)10^4 = (32)*10^4=(2^5)*10^4

60 minutes________________(32)10^4 + (32)10^4 = (64)*10^4=(2^6)*10^4

As you can see, solving this way is pretty complex.Avoid this if you can