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

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: