MathMaster logo

MathMaster

  1. Home
  2. general
  3. describe a real life situation that can be modeled by a function a relation in which every input value corresponds to only
Question

Describe a real-life situation that can be modeled by a function (a relation in which every input value corresponds to only one output value). The situation must be different from the examples provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your relation does, in fact, represent a function. 2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example. 3. Identify the domain and range of your function, using proper mathematical notation.

251

likes
1254 views

Answer to a math question Describe a real-life situation that can be modeled by a function (a relation in which every input value corresponds to only one output value). The situation must be different from the examples provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your relation does, in fact, represent a function. 2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example. 3. Identify the domain and range of your function, using proper mathematical notation.

Expert avatar
Nash
4.9
87 Answers
Real-life Situation:
A car rental company charges a fixed fee for renting a car for a certain number of days, and an additional daily rate for any extra days beyond the initial rental period.

Function Representation:
Let's say we have a car rental company that charges a fixed fee of $50 for renting a car for up to 3 days, and an additional $10 per day for any extra days beyond the initial rental period.

Input and Output Values:
In this situation, the input value would be the number of days a car is rented for, denoted by x. The output value would be the total cost of renting the car for those number of days, denoted by y.

Function Representation:
To create a function that models this relationship, we can use the piecewise function notation:

y = \begin{cases} 50 & \text{if } x \leq 3 \ 50 + 10(x-3) & \text{if } x > 3 \end{cases}

This function can be read as follows: for x less than or equal to 3, the cost of renting the car is $50. For x greater than 3, the cost is $50 plus $10 for each extra day beyond 3.

Domain and Range:
The domain of this function would be the set of possible values for x, which in this case would be the set of positive integers representing the number of days a car is rented for: D = \{1, 2, 3, 4, 5, ...\}

The range of this function would be the set of possible values for y, which in this case would be the set of positive integers representing the total cost of renting a car for a given number of days: R = \{50, 60, 70, 80, ...\}

Answer: The real-life situation of a car rental company can be modeled by the function y = \begin{cases} 50 & \text{if } x \leq 3 \ 50 + 10(x-3) & \text{if } x > 3 \end{cases} . The domain is D = \{1, 2, 3, 4, 5, ...\} and the range is R = \{50, 60, 70, 80, ...\} .

Frequently asked questions (FAQs)
What is the derivative of f(x) = 3x^4 + 2x^3 - 5x^2 + 7x - 1?
+
What is the probability of selecting a red marble from a bag containing 5 red marbles, 3 blue marbles, and 2 green marbles?
+
What are the key characteristics of the cotangent function f(x) = cot x?
+
New questions in Mathematics
Find two natural numbers whose sum is 230 and their difference is 10. Set up the system and solve it.
The strength of Kefexin oral suspension is 100 mg/ml. Nora has been prescribed cefalexin at a dose of 50 mg/kg/day divided in two single doses. Nora weighs 14 kg. How many milliliters of solution for Nora should be given as a single dose?
CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.
the value of sin 178°58'
solve the following trigo equation for 0°<= x <= 360°. sec x =-2
The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?
There are 162 students enrolled in the basic mathematics course. If the number of women is 8 times the number of men, how many women are there in the basic mathematics course?
If you randomly selected one person from the 900 subjects in this study, what is the probability that the person exhibits the minimum BMI?
prove that if n odd integer then n^2+5 is even
I need to know what 20% or £3292.75
sin 30
Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.
3. A rock is dropped from a height of 16 ft. It is determined that its height (in feet) above ground t seconds later (for 0≤t≤3) is given by s(t)=-2t2 + 16. Find the average velocity of the rock over [0.2,0.21] time interval.
Convert 9/13 to a percent
A function is considered exponential when it has a base with positive values greater than zero and different from one, where the exponent is an unknown. An important characteristic of exponential functions is that they show rapid growth or decay as an independent variable increases or decreases. Given the function 25^(x+3)=125, it is calculated that x has the value of
16.What payment (deposit) made at the end of each month will accumulate to $10473 in 13 years at 7.9% compounded monthly? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
y′ = 2x + 3y x′ = 7x − 4y x(0) = 2 y(0) = −1 sisteminin ¸c¨oz¨um¨un¨u bulunuz. (Lineer Denk. Sis.)
2+2020202
56 × 12 = 672. How should you adjust this answer 672 to determine 57 × 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
A gas is leaking at 3.5ft3/min in a room of 2.9m by 6.9ft by 15.7m. How long would it take (in seconds) for 22% of the room to reach the LFL, if the gas has a LFL of 2.51%?

You might be interested in