Answer:
The function
P(t) = 2000e^0.0011552453t or 2000e^(In2/60)t
Step-by-step explanation:
A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.
The function is gotten as:
P(t) = Poe^kt
Where P(t) = Number of the bacteria after t minutes
P(o) = Initial number of the bacteria
e = Euler number
k = Growth rate
t = time
We have to find k
We are told that the culture contains 2000 bacteria initially and doubles every 60 minutes.
Hence,
n(60) = 2 × 2000
n(60) = 4000
This:
4000 = 2000 × e^k × 60
4000/2000 = e^60k
2 = e ^60k
In 2 = In e^60k
In 2 = 60k
k = In2/60
k = 0.011552453
Hence, the function P(t) = 2000e^0.0011552453t or 2000e^(In2/60)t
