Question

Consider a colony of E.Coli bacteria that is growing exponentially. A microbiologist finds that, initially, 1,000 bacteria are present and 50 minutes later there are 10,000 bacteria. a) Find expression for the number of bacteria Q(t) after t minutes. b) When will there be 1,000,000 bacteria?

Answer 1

Answer: a)
`N(t) = 10^3\exp(0.046(1)/(min)t)`

b) 1,000,000 bacteria at t = 150 min

Explanation:

Hi!!

A colony that grows exponentially has a number of bacteria:

`N(t) = N_0 \exp(\lambda t)`

In this case at time t = 0:

`N(0)=N_0=10^3`

We need to find the value of λ. We use the data:

`N(t=50\;min)10^4 = 10^3\exp(\lambda \;50\;min)`

`ln(10)=2.3=\lambda\;50\;min\\\lambda= (0.046)/(min)\\N(t) = 10^3\exp((0.046)/(min)t)\\`

To find when there will be 1,000,000 bacteria:

`10^6=10^3\exp((0.046)/(min)t)`

`\ln(10^3)=3\ln(10) = (0.046)/(min)t`

`t = 150\;min`