Answer:
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 .
