WGU C957 Applied Algebra OA Actual Real Exam Questions and Answers

A local business is looking to become a franchise. The company wants to predict the number of franchises, F, given a certain number of years, Y. This prediction is modelled by the function F( Y). What can be concluded by F(5) = 10? In 5 years, there will be 10 open stores. A bank begins a marketing campaign to increase its number of customers. Each month, all new customers are put into a drawing. One customer then receives a $50 credit in a checking account. The amount of money given away in the drawing, G, is a function of the number of months, M, the drawing has been going on for. What is the correct function notation to represent the amount of money given away after the drawing has been going on for 5 months? G(5) = 250 The volume of calls, V( h), at a particular customer service centre can be written as a function of the number of hours after opening each day, h. What would the ordered pair (6,8) represent for this function? There were 8 calls 6 hours after opening. A company has developed two functions, L( t) and M( t), that determine the least amount and most amount, respectively, of revenue it will make in any given month in dollars (with t = 1 corresponding to January). What can the company reasonably conclude if L(2) = 3,000 and M(2) = 5,000? In February, it will make between $3,000 and $5,000. A server at a restaurant has realized that tips, T, in dollars are related to the number of hours, h, that have been worked on any given day. Tips can be modeled by the function T( h) = X. How can this function be interpreted? If the server works h hours, the tips will be $ X. A company pays its employees a base salary each month plus a commission, C, based on the number of sales, s, made by an employee during the month. An employee made 8 sales in the last month and received a commission of $1,600. How would this be represented in function notation? C(8) = 1600 Below is a growth graph of a business. It compares gross growth and net growth. What can be said about the growth between the years of 2012 and 2014? Both gross and net growth increased. The graph below shows the three-month average percentage year-on-year growth for real total pay for the years 2010–2016, along with the Office for Budget Responsibility's (OBR's) growth forecast for the years 2016–2021. What can be concluded from this graph? The OBR forecasts the growth will remain above 1% between 2016 and 2021. The following graph shows the profits of a company for the last fiscal year. Approximately how much have the company's profits increased over the last year? 30% Black Monday occurred on October 19, 1987, and represents the single largest decline of the Dow Jones average in history. The function f represents a seven-month period during which Black Monday occurred. The function value f(1) represents the Dow Jones average in June of 1987. Which function value represents the Dow Jones average during the month when Black Monday occurred? f(5) The unemployment rate in Poland for the time period from 1990 to 2012 is shown in the graph below using the function U( t) (measured as a percentage), where t is the year. For example, U(1990) is the unemployment rate for the year 1990. What can be concluded based on this graph? The largest two-year increase in unemployment was from 1990 to 1992. The graph of the function C below represents the number of coal miners in the United States from 1985 to 2015.C( y) represents the number of coal miners in the United States in the year y. For example, C(1985) shows there were 170,000 coal miners in the United States in 1985. Which interpretation of the function C is accurate? C(2000) represents 70,000 coal miners in 2000. The following table compares the number of employees hired and the number of employees dismissed over an 11-year period for a certain business. Year# Hired# Dismissed 2009 30 5 2014 15 5 2015 20 6 2016 10 2 2017 10 7 What can be concluded from this table? More employees were hired than dismissed each year. A company has the following information on last quarter's sales (month 7 refers to July): Month Sales (in thousands of dollars) 7 303 8 328 9 333 What was the average rate of change over the entire quarter (from July to September)? Sales increased an average of $15,000 per month. An IT firm generates the following numbers to estimate its revenue in thousands of dollars based on the number of employees working on a project. Employees Revenue (in thousands) 10 $12.40 20 $21.99 30 $30.74 40 $36.01 50 $38.43 Which conclusion can be made by examining the average rate of change between consecutive rows? The revenue is increasing at slower and slower rates in relation to the number of employees. An airplane was cruising at an altitude of 39,000 feet and descended as shown in the table below. Descent of Airplane Altitude of Airplane (ft.) Time (min.) 39,000 0 33,000 10 27,000 20 21,000 30 15,000 40 9,000 50 3,000 60 What can be concluded from this table? The airplane had a descent rate of 600 ft./min. The function table below shows a company's revenue function (R) and expense function (E) for each month. In the second row, R(1) is the revenue total for January, and E(1) is the expense total for January. Monthly Revenues and Expenses Month (m) Revenues R(m) Expenses E(m) 1 (Jan.) $2,000 $2,200 2 (Feb.) $3,220 $3,957 3 (Mar.) $2,579 $2,504 4 (Apr.) $4,100 $1,675 5 (May) $5,328 $2,122 6 (June) $6,745 $1,990 7 (July) $5,995 $2,111 8 (Aug.) $10,200 $3,183 9 (Sept.) $9,455 $4,129 10 (Oct.) $12,337 $927 11 (Nov.) $10,234 $3,786 12 (Dec.) $7,195 $2,199 Which conclusion can be made about this function table? The highest profit occurred during October. The original value of a company car bought in January of 2006 was $22,800. Below is a function table that tracks the value of the car V( y) as it depreciates. Depreciation of Company AutomobileYear (y) Value (V(y)) 2006$ 22,800 2007$ 18,240 2008$ 15,504 2009$ 13,178 2010$ 11,201 2011$ 9,521 2012$ 8,093 2013$ 6,879 2014$ 5,847 2015$ 4,970 V(2007) = $18,240 is the value of the car from January to December of 2007. Which other conclusion can be reached from this table? V( y) decreases the most from 2006 to 2007. The salvage or depreciated value, V, of a new truck purchased for $58,000 is given by the linear function V( t) = 58,000 – 4,000 t, where t is the time in years between 0 and 10. What is the correct interpretation of V(3)? The truck's depreciated value after 3 years is $46,000. In the function C( x) = 21.25 + 0.25 x, C( x) represents the total cost, in dollars, for a passenger to ride a shuttle service for x miles. What is the total cost for a passenger to ride the shuttle for 50 miles? $33.75 A company's total monthly cost is given by the linear function C( x) = 11,000 + 550 x , where C is the total monthly cost and x is the number of units produced each month. The graph of the function is given below: What does the y-intercept represent in this situation? If 0 items are produced, the monthly cost is $11,000.00. A cable company, a satellite dish company, and a streaming service all offer TV viewing plans based on the number of channels, c, on the plan. The price of each plan is given below: Cable: P( c) = 3 c + 60Satellite dish: P( c) = 4 c + 35Streaming service: P( c) = 5 c + 50 Which company's cost per additional channel is most expensive? Streaming service The number of gym memberships since January 1, 2015, for a particular gym is given by the function N( x) = 100 + 11 x, where N is the number of gym members x months after January 1, 2015. How can the slope be interpreted? Each month, 11 members join the gym. The pricing models of four contractors are given below, where t is the number of hours worked and P is the total cost of the job. Contractor A: P( t) = 100 + 20 tContractor B: P( t) = 99 + 25 tContractor C: P( t) = 50 + 35 tContractor D: P( t) = 80 + 25 t Which contractor gives the cheapest hourly rate? Contractor A An appliance manufacturer has determined that the profit, P( x), that it makes in manufacturing and selling x dishwashers can be determined from the function in the graph below. How many dishwashers must the company manufacture and sell in order to make a profit of $80,000? 130 The profit function P( x) gives a company's total profit (in millions of U.S. dollars) for x products produced (in thousands). The graph of P( x) is below: At which number of products produced does the company stop being profitable? About 4,500 items A big box store found its number of customers, C, in thousands on Saturday is predicted by the time of day in hours, t. In the graph below, t = 0 corresponds to midnight of the current day and t = 24 corresponds to midnight of the next day. How should the average rate of change from t = 8 to t = 10 be interpreted? There are, on average, 1,000 more customers per hour. The profit for a manufacturer of a certain product is given by the function P( x) = –4 x 3 + 12 x 2 + 16 x, where P is the total profit (in thousands of dollars) for x items produced (in thousands). What is the average rate of change from x = 4 to x = 8? Profit decreases by $288,000 per 1,000 items produced. The graph below represents the projected year-end assets, A( t), in the Social Security trust fund in trillions of dollars, where t represents the number of years since 2000. In the graph, t is defined between and including 0 to 50. At which value of t is the fund increasing the most rapidly? About t = 0 A local coffee shop found that its number of customers, N, can be predicted by the time of day in hours, t. The opening time of 5:00 a.m. corresponds to t = 0. How should the graph be interpreted between t = 5.5 and t = 9? Between 10:30 a.m. and 2:00 p.m., the number of customers is increasing faster and faster and then increasing slower and slower. The total profit, P( x), in thousands of dollars from the production of x thousands of laptop computers is given by the graph below. For this graph, x must be greater than or equal to 5. How many laptops must be produced to maximize the profit? 10,000 For the years since a department store has been open, its annual revenue, R, (in millions of dollars) can be modeled by the function graphed below, where t is the number of years since the store opened. How should the maximum revenue be interpreted? About 6 years after the department store opened, the store earned a maximum revenue of about $1,600,000.00. The population of the United States in millions of people can be estimated with the function P( t) = 282(1.01) t, where t = 0 represents the population, P, in the year 2000, and t is measured in years. What does P(–2) represent? P(–2) represents the population in 1998, which was approximately 276 million people. A high-interest loan company uses the function L( d) = 100 e 0.02 d to calculate late fees, L, for payments overdue by d days. What does L(67) represent? L(67) is the amount due in late fees for a payment that is 67 days overdue, which would be $381.90. A bank uses the function A( t) = 1000(1.023) t to calculate an account balance, A, after t years. What is the average rate of change of the account balance from t = 2 to t = 12? The account will increase by $26.72, on average, each year. A scientist found a sample of carbon-14 and knows the graph below models the exponential decay of carbon-14, where t is time measured in years and y is the amount of carbon-14 left in the sample in grams. What would the average rate of change over the time interval of t = 100 to t = 700 represent, and would that rate be positive or negative? It represents the annual change in the number of grams of carbon-14 between 100 and 700 years. The rate is negative. A company uses the function C = 15 e –n + 10, which is shown in the graph below, to model the average cost per toy produced, C, where n is the number of toys produced. How should this horizontal asymptote be interpreted? As the number of toys produced increases, the average cost per toy tends toward $10. Two medical operations are being compared to determine which is better for patients. Below is a graph of the chance of infection after operation (in percentage) for the first option (shown with a solid curve) and for the second option (shown with a dashed curve). Both curves are shown over time since 1950, in years. As time has gone on, which is the better operation? Operation 1 is better because the chance of infection has dropped to a steady 10% since around the year 2000.