A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 570. (a) Find an expression for the number of bacteria after t hours. P(t)

p(t)=100e^ln5.7t

Explanation:

The growth rate of bacteria is directly proportional to its size and shows the exponential growth. The initial bacteria amount is 100 and later increased to 570.

The number of bacteria after t hours is

p(t)=100e^kt where k is the relative growth rate. and t is the time.

Here p (t) = 570 and t = 1 hour, then K =

 420=100e^k(1)  

K = ln(5.7)

Put the value of K in original equation then,

p(t)=100e^ln(5.7)t

Thus, the expression for the number of bacteria after t hours is p(t)=100e^ln(5.7)t .

from the original order (top to bottom) the new order will go

1 (founder)

4 (hawk)

2 (mutate)

3 (next generation)