Write a Linear Equation for the Value of this Printer Over Time

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SUMMARY

The discussion centers on formulating a linear equation to represent the depreciation of a high-volume printer, copier, and scanner purchased by a school district for $24,000, with an expected residual value of $2,000 after 10 years. The derived equation is V(t) = -2,200t + 24,000, where V is the value of the equipment at time t in years. Participants emphasize the importance of verifying the equation by checking the values at t=0 and t=10, which correspond to the initial and final values of the equipment, respectively. The conversation also highlights the need for continuity in forum discussions to avoid redundancy.

PREREQUISITES
  • Understanding of linear equations and their components (slope and intercept).
  • Familiarity with the concept of depreciation in asset management.
  • Basic algebraic manipulation skills.
  • Knowledge of the coordinate system for plotting points (t, V).
NEXT STEPS
  • Explore the concept of depreciation methods in accounting, focusing on straight-line depreciation.
  • Learn how to graph linear equations using software tools like Desmos or GeoGebra.
  • Investigate the implications of asset value over time in financial forecasting.
  • Review best practices for engaging in online forums to enhance discussion quality and continuity.
USEFUL FOR

Students in mathematics or finance, educators teaching linear equations, and individuals involved in asset management or accounting who need to understand equipment depreciation.

nycmathguy
Homework Statement
Write a linear equation for the given application.
Relevant Equations
y = mx + b
Write a linear equation.

A school district purchases a
high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment
during the 10 years it will be in use.

Solution:

Let t = time in years

(V - 24,000)/(t - 0) = (2,000 - 24,000)/(10 - 0)

(V - 24,000)/t = -2,200

V - 24,000 = -2,200t

V(t) = -2,200t + 24,000

You say?
 
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Please read the responses to your prior posts and learn from them before you swamp the forum with so many similar questions.
 
Last edited:
nycmathguy said:
Homework Statement:: Write a linear equation for the given application.
Relevant Equations:: y = mx + b

V(t) = -2,200t + 24,000

You say?
Two things:
  1. Questions like this are very easy to check. Since the equation is that of a line, if your equation yields two points correctly, you know you have the right equation. What is V(0)? This should be the initial value of the equipment. What is V(10)? This should be the value of the equipment at the end of its projected life.
  2. Didn't you post the exact same question before? Instead of starting a new thread for the same question, continue with the old thread.
 
The exercise description gives two point, in the variable point of (t,V). No actual year identity is mentioned; just number of years. The two given points described are (0, 24000) and (10, 2000).

Notice one of the 'given' points IS the V-axis intercept! (The two given points will give you the slope for the line).

Think about that, and look at your work and decide if it fits or not, and maybe you will determine if you succeeded in the exercise or not.
 
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Mark44 said:
Two things:
  1. Questions like this are very easy to check. Since the equation is that of a line, if your equation yields two points correctly, you know you have the right equation. What is V(0)? This should be the initial value of the equipment. What is V(10)? This should be the value of the equipment at the end of its projected life.
  2. Didn't you post the exact same question before? Instead of starting a new thread for the same question, continue with the old thread.
Every problem is different in one way or another. Thus one has a slight twist, I think.
 
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Thank you everyone.
 
nycmathguy said:
Every problem is different in one way or another. Thus one has a slight twist, I think.
But what we're trying to get you to do is to think about the similarities between them.
 
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Mark44 said:
But what we're trying to get you to do is to think about the similarities between them.
Yeah, I know.
 
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nycmathguy said:
Homework Statement:: Write a linear equation representing the situation at hand.
Relevant Equations:: y = mx + b

A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use.
The above is directly from the thread you posted about 4 days ago.

If there is a difference, indeed it is very subtle .
 

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