How Fast Do Bacteria Multiply in a Culture?

In summary, the bacteria population initially starts with 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000 e^{kt} for some constant k. To find the value of k, we can use the given information to solve for k. When t = 0.5 hour, p(t) = 4000. By plugging in these values, we can solve for k and find that k = ln(2)/0.5 = 1.386294361.
  • #1
Niaboc67
249
3
A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000 e^{kt} for some constant k. (You will need to find k to answer the following.)

Find the size of the baterial population after 40 minutes.

Find the size of the baterial population after 10 hours.

Soltn:
When t = 0.5 hour, p(t) = 4000, so we have

4000 = 2000e^(0.5k)

2 = e^(0.5k)

ln(2) = 0.5k

k = ln(2)/0.5 = 1.386294361

Where did 4000 part come from?

Thank you
Where
 
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  • #2
Niaboc67 said:
A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000 e^{kt} for some constant k. (You will need to find k to answer the following.)

Find the size of the baterial population after 40 minutes.

Find the size of the baterial population after 10 hours.

Soltn:
When t = 0.5 hour, p(t) = 4000, so we have

4000 = 2000e^(0.5k)

2 = e^(0.5k)

ln(2) = 0.5k

k = ln(2)/0.5 = 1.386294361

Where did 4000 part come from?

Thank you
Where
A bacteria culture initially contains 2000 bacteria and doubles every half hour.
 
  • #3
@SteamKing but it's 40 minutes so shouldn't it be a little more than that?
 
  • #4
Niaboc67 said:
@SteamKing but it's 40 minutes so shouldn't it be a little more than that?

No. You are still just working out the value of k. You have not gotten to the 40 minute problem yet.
 

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