/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 Sketch a rough graph of the mark... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Sketch a rough graph of the market value of a new car as a function of time for a period of 20 years. Assume the car is well maintained.

Short Answer

Expert verified
The car's market value sharply declines initially, then slows, and stabilizes after about 15 years.

Step by step solution

01

Understand the Problem

Before sketching the graph, consider the typical behavior of a car's market value over time. A new car depreciates quickly in the first few years, then the value decline slows down, and may even stabilize as it becomes a classic.
02

Identify Key Features of the Graph

Identify important aspects for your graph: Initial high value (purchase price), steep initial decline, gradual decline, and potential stabilization at a low value.
03

Draw the Axes

Draw two perpendicular lines; label the horizontal axis as 'Time (years)' from 0 to 20, and the vertical axis as 'Market Value.' Start at the market value when the car is new.
04

Plot the Initial Point

Start by plotting a point at the top of the y-axis to represent the initial purchase price of the car. This is where time equals zero.
05

Illustrate the Early Steep Decline

From the initial point, draw a curve that quickly slopes downwards to indicate rapid depreciation over the first 3 to 5 years.
06

Show the Gradual Decline

Beyond the initial steep decline, continue the curve with a gentler slope downwards up to about 15 years. This represents slower depreciation as the car ages.
07

Indicate Stabilization

After approximately 15 years, make the curve almost flat or very slightly declining, showing that the car's value stabilizes as it becomes a possibility to be considered a classic.
08

Review and Label

Review the sketch to ensure it reflects the expected depreciation pattern and label significant points like the initial purchase price and the stabilization period.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Depreciation
Depreciation is a decline in the value of an asset over time, often due to wear and tear, age, or obsolescence. When it comes to cars, depreciation is a crucial concept because vehicles tend to lose a significant portion of their value shortly after being purchased. This value loss happens most rapidly in the first few years.

Several factors influence depreciation, including:
  • Make and model
  • Condition and mileage
  • Market demand
  • Technological advances
Depreciation can be calculated and represented in various ways, but commonsense understanding involves observing how the market perceives an aged asset. Businesses often use depreciation calculations to manage their finances and tax obligations, employing methods like straight-line or accelerated depreciation. For used car buyers and sellers, understanding depreciation helps in making informed purchasing and selling decisions.
Function of Time
When we talk about the function of time concerning market value, we are essentially evaluating how an asset's worth changes as time progresses. Time functions in these scenarios typically include a time-based component on one axis and the asset's value on the other.

For a car, this relationship is almost always visualized using a graph, where:
  • The x-axis represents time (often in years)
  • The y-axis represents the car's market value
In the initial years, cars usually experience rapid devaluation. After this steep initial decline, depreciation tends to become more gradual. Many factors can further alter this time-value relationship, such as market trends or economic conditions. As cars age significantly, they can sometimes stabilize or even increase in market value, especially if they become rarities or classics.
Classic Car
The term 'classic car' often conjures images of vintage vehicles with timeless elegance and historical significance. But what defines a classic car goes beyond just age; it involves rarity, desirability, and cultural value. Generally, a car might be considered a classic a couple of decades after its original manufacture, often around the 20-year mark.

Characteristics that can qualify a car as a classic include:
  • Unique design or technological innovation
  • Limited production numbers
  • Cultural impact or notable history
  • Dedicated enthusiast community
As a car approaches classic status, its market value curve often flattens out or may even start to incline, in contrast to newer cars. A once common model may gain value due to nostalgia or a resurgence in popularity, adding a layer of complexity to its depreciation timeline. Thus, understanding when and how a vehicle becomes a classic is essential for collectors and enthusiasts alike.

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