Hello, if you have any need, please feel free to consult us, this is my wechat: wx91due
BUSINESS MATHEMATICS (QTS0103)
CONTINUOUS ASSESSMENT 1
INDIVIDUAL ASSIGNMENT (30%)
Question 1 (10 marks)
(a)Solve the following equation. Give your answer to 2 decimal places (if applicable).
4/x − 15 = −2x + 2/1[2 marks]
(b)Solve the following inequalities:
(i) −3 ≤ 3/x+1 ≤ 2[2 marks]
(ii) |2x − 5| ≥ 10[2 marks]
(c)Given: f(x) = 3x and g(x) = x2 − 1. Find the value of: fog(1)[2 marks]
(d)Determine the domain of the function: f(x) = x2-9/5[2 marks]
(Total 10 marks)
Question 2 (10 marks)
(a)Find the equation of the line that passes through the point (5, –5) and is parallel to the line with equation y = -2x – 1.[3 marks]
(b)Find the point of intersection(s) of the lines of the functions f(x) = 5x + 6 and g(x) = x 2 + 2x. Provide your workings and answer(s) to 2 decimal places when applicable.
(c)Your firm had sales of $30,000 in its first year of operation. If sales increase by 10% per year thereafter, determine your company’s sales in the tenth year and its total sales over the twenty years of operation. Give your answers to the nearest dollar.[4 marks]
(Total 10 marks)
Question 3 (10 marks)
(a)Your firm manufactures office tables at cost of $50 per unit and sells them for $80 per unit. With a monthly fixed cost of $120,000, determine your firm’s monthly break-even quantity and break-even revenue.[3 marks]
(b)Solve the following equations for x. Provide your answer(s) to 3 decimal places when applicable.
(i) 2e4x-1 = 12[2 marks]
(ii) ln x 2 + ln 3 = 5[2 marks]
(c)Your firm purchased a machine for $250,000. After 2 years, the value of the machine decreased to $150,000. If the machine’s value decreases exponentially, what will the machine’s value be after 10 years? Provide your workings to 3 decimal places and answer to the nearest dollar.[3 marks]
(Total 10 marks)