Part 1 1. Write a demand and a supply curve expressed in the form of an exponential and logarithmic functions respectively. Demonstrate graphically or otherwise, that the functions reflect all the characteristics of a demand and supply curve. 2. a. Solve the linear inequality: 2(5 – ?) ≤ 3(5 – ?) - 7 ?. b. Hence or otherwise, represent your solution set on a number line. 3. Solve the system of linear inequalities: 4?+2? ≥8 ? −4>? 4. Windies Cricket manufactures Windies supporter jerseys. The quantity q, of these jerseys demanded weekly is related to the wholesale price per jersey p, by the following equation: ?=−0.006?+15 The weekly total cost incurred by Windies Cricket for producing q jerseys is: ?(?)=38?−0.02?2+30,000 a. Determine an expression to represent the weekly Revenue function. b. Determine an expression to represent the weekly Profit function. c. Calculate the weekly Revenue when ten dozen jerseys are produced and sold. d. Will Windies Cricket record a loss or profit if they were to produce and sell 2450 jerseys? e. If Windies Cricket wishes to maintain a total cost less than $42,000.00, what range(s) of Windies jerseys should be produced. f. Calculate the equilibrium price and quantity for Windies jerseys. Part 2 1. Given that ?=(?3−8)45, answer the following questions: a. Determine the inverse for the above function. b. State any six (6) possible values that will be included in the domain of the above function. 2. Classify the following sequences: a. ?−5,5,?+5,……… b. ?, ?2−1,?3−2?+1?,……. 3. James has two job offers. Massy offers James the job with an initial annual salary of $38,800.00 along with guaranteed annual increases of $3,200.00 for the first five years. Unicomer offers him an initial annual salary of $47,600.00 along with guaranteed annual increases of $1,000.00 for the first five years. a. Compare and contrast the two offers to determine the company that offers the highest annual salary for the fifth year of employment. Show all necessary calculations. b. Compare and contrast the two offers to determine the company that proposes the most (total) renumeration over James’ first five years of employment. Show all necessary calculations. c. Which company should James take up his employment with if both companies offer him an annual salary of $60,000.00 in his sixth year? Why? 4. It has been projected by UNDP that the population of Wakanda will increase by 0.8% for each of the next quarters for 5 years. If Wakanda registered a population of 25,000 in the second quarter of 2023 (base period): a. What is the expected population in Wakanda after the third quarter in 2025? b. What is the expected population in Wakanda after the first quarter in 2030?
Part 1
1. Write a demand and a supply curve expressed in the form of an exponential and logarithmic functions respectively. Demonstrate graphically or otherwise, that the functions reflect all the characteristics of a demand and supply curve.
2. a. Solve the linear inequality: 2(5 – ?) ≤ 3(5 – ?) - 7 ?.
b. Hence or otherwise, represent your solution set on a number line.
3. Solve the system of linear inequalities:
4?+2? ≥8
? −4>?
4. Windies Cricket manufactures Windies supporter jerseys. The quantity q, of these jerseys demanded weekly is related to the wholesale price per jersey p, by the following equation:
?=−0.006?+15
The weekly total cost incurred by Windies Cricket for producing q jerseys is:
?(?)=38?−0.02?2+30,000
a. Determine an expression to represent the weekly Revenue function.
b. Determine an expression to represent the weekly Profit function.
c. Calculate the weekly Revenue when ten dozen jerseys are produced and sold.
d. Will Windies Cricket record a loss or profit if they were to produce and sell 2450 jerseys?
e. If Windies Cricket wishes to maintain a total cost less than $42,000.00, what range(s) of Windies jerseys should be produced.
f. Calculate the equilibrium price and quantity for Windies jerseys.
Part 2
1. Given that ?=(?3−8)45, answer the following questions:
a. Determine the inverse for the above function.
b. State any six (6) possible values that will be included in the domain of the above function.
2. Classify the following sequences:
a. ?−5,5,?+5,………
b. ?, ?2−1,?3−2?+1?,…….
3. James has two job offers. Massy offers James the job with an initial annual salary of $38,800.00 along with guaranteed annual increases of $3,200.00 for the first five years. Unicomer offers him an initial annual salary of $47,600.00 along with guaranteed annual increases of $1,000.00 for the first five years.
a. Compare and contrast the two offers to determine the company that offers the highest annual salary for the fifth year of employment. Show all necessary calculations.
b. Compare and contrast the two offers to determine the company that proposes the most (total) renumeration over James’ first five years of employment. Show all necessary calculations.
c. Which company should James take up his employment with if both companies offer him an annual salary of $60,000.00 in his sixth year? Why?
4. It has been projected by UNDP that the population of Wakanda will increase by 0.8% for each of the next quarters for 5 years. If Wakanda registered a population of 25,000 in the second quarter of 2023 (base period):
a. What is the expected population in Wakanda after the third quarter in 2025?
b. What is the expected population in Wakanda after the first quarter in 2030?
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