# L100 Economics Assignment-City, University of London

Instructions to students : All questions are compulsory.

Materials:

Dictionaries are not permitted.

Question 1.

Let f (t) = Aeat. Suppose that f (0) = 4500 and f (4) = 6000.

(a) Find the value of A and a (correct to 2 decimal places).

(b)Deduce the value of f (10) (correct to 2 decimal places).

Question 2.

Using the product rule, quotient rule or chain rule, diﬀerentiate each of the following functions

a) y = 2x4 ln x

b) y = ln(2x2 + 3)

### Question 3: L100 Economics Assignment-City, University of London

Find and classify the stationary points of the function f (x) = x2 + 3x + 7.

Question 4.

The cost C of making Q goods is given by Find the quantity Q that minimizes the cost C.

Question 5.

Consider the system of linear equations a)Write this system in matrix form Ax = b.

b)Compute the determinant |A|.

c)Compute the inverse matrix A−1.

d)Use (c) to solve this system of linear equations.

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