# Thread: Exponential growth of bacteria

1. ## Exponential growth of bacteria

The number of of bacteria $N$ in a colony after $t$ minutes is given by $N=10 000e^{0.05t}$ Find the rate at which the colony increases when

i) $t=10$

ii) $N=2000$

2. Originally Posted by nerdzor
The number of of bacteria $N$ in a colony after $t$ minutes is given by $N=10 000e^{0.05t}$ Find the rate at which the colony increases when

i) $t=10$

ii) $N=2000$
natural exponential growth ...

$
\frac{dN}{dt} = 0.05N
$

3. Originally Posted by skeeter
natural exponential growth ...

$
\frac{dN}{dt} = 0.05N
$

Care to explain further?

4. The number of of bacteria in a colony after minutes is given by Find the rate at which the colony increases when

i)

Differentiate 0.05*1000 N'=500e^0.05(10)=824.36

ii)

2000=500e^0.05
4=e^0.05
In4=Ine^o.o5

In4/0.05=27.7

5. In a certain bacteria culture, the rate of increase is proportional to the number of bacteria present

a) If the number doubles in 3 hours. Find the hourly growth rate
b) How many bacteria after 9 hours? If the original population is 104
c) After how many hours are there $4 * 10^4$ bacteria

6. Originally Posted by BobCalc

ii)

2000=500e^0.05
4=e^0.05
In4=Ine^o.o5

In4/0.05=27.7
How odd. The answers say 1000/min