Answer:
a)
b) 54.225 square centimeters.
c) 2.52 hours
Step-by-step explanation:
The population growth law is:
In which P(t) is the population after t hours, is the initial population and r is the growth rate, as a decimal.
In this problem, we have that:
The colony occupied 2 square centimeters initially, so
The colony triples every 4 hours. So
(a) An expression for the size P(t) of the colony at any time t.
We have to find the value of r. We can do this by using the P(4) equation.
Applying ln to both sides, we get:
So
(b) The area occupied by the colony after 12 hours.
(c) The doubling time for the colony?
t when .
Applying ln to both sides