Mathematics 2

Yanıt Açıklaması: We know the initial population and that at the population is Hence, from So after 12 hours, The correct answer is A.

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

Yanıt Açıklaması: 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

Yanıt Açıklaması: The substitution u=1+e x gives du=e x dx. Therefore we have

Yanıt Açıklaması: Let then also the boundaries become and Substituting these values into the question we have Hence the correct answer is E.

Yanıt Açıklaması: The area can be calculated as So the correct answer is D.

Yanıt Açıklaması: 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.

Yanıt Açıklaması: the correct answer is A.

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Yanıt Açıklaması: The consumer surplus is evaluated taking into account the demand function since the equilibrium point we have Correct answer is B

Yanıt Açıklaması: 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.

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Yanıt Açıklaması: It is known that the general form of a first order differential equation so  the  equation is a differential equation. Correct answer is E.

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Yanıt Açıklaması: the correct answer is B.

Yanıt Açıklaması: Inserting the Lorenz function into the formula for the Gini index we obtain Thus, the right answer is E.

Yanıt Açıklaması: The price may be found as . Using the integral formula for the producer surplus, we obtain: Therefore the correct answer is the C option.