We know the initial population

and that at

the population is

Hence, from

So after 12 hours,

The correct answer is A.

If we set  then we obtain  This substitution gives the following integral, 

The general solution of the differential equation is

from the previous solution. To satisfy the first initial condition we set

 in the general solution; thus

must satisfy

 To use the second initial condition we must first  differentiate the equation

This gives

Then, setting

we obtain

By solving the equations involving

together we find that

Using these values in the general solution, we obtain the solution

The substitution u=1+e^x gives du=e^xdx. Therefore we have

Let

then

also the boundaries become

and

Substituting these values into the question we have

Hence the correct answer is E.

The area can be calculated as

So the correct answer is D.

As before, we only need to apply the formula for the future value of an income. Since the time period is      T = 3 and the interest rate gives r = 0,15, we have

Hence the correct solution is B.

 the correct answer is A.

The consumer surplus is evaluated taking into account the demand function since the equilibrium point

we have

Correct answer is B

Let us use the change of variables method. Let

and the upper bound becomes

and the lower bound becomes

Substituting these values into the integral we get

which gives the correct answer B.

It is known that the general form of a first order differential equation

so  the  equation

is a differential equation.

  Correct answer is  E.

the correct answer is B.

Inserting the Lorenz function into the formula for the Gini index we obtain

Thus, the right answer is E.

The price may be found as

. Using the integral formula for the producer surplus, we obtain:

Therefore the correct answer is the C option.