Abiologist observed that a certain bacterial colony obeys the population growth law and that the colony triples every 4 hours.

if the colony occupied 2 square centimeters initially, find:

(a) an expression for the size p(t) of the colony at any time t.

(b) the area occupied by the colony after 12 hours.

(c) the doubling time for the colony?

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

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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