**Instructions to students : All questions are compulsory.**

**Materials: **

Dictionaries are not permitted.

## TASK: L100 Economics Assignment

**Question 1.**

Let f (t) = Ae^{at}. 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 = 2x^{4} ln x

b) y = ln(2x^{2} + 3)

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

Find and classify the stationary points of the function f (x) = x^{2} + 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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